微积分
极限、导数、最优化与函数性质。
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5) $(-6.2)+(-6.9)$ a) $-5.7$ b) $-13.1$ c) $-9.6$ d) $-7.1$ 6) $(-4.3)-…
B) -13.1 ### Problem 6: $(-4.3)-(-5.7)$
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lesson 2: absolute value & operations with integers directions: solve e…
1. $8$ 2. $10$ 3. $-7$ 4. $10$ 5. $11$ 6. False 7. True 8. $-7, -5, 4$ 9. $-110$ (Note: For the drawing components: 1. Draw the hair for answer 8 2. Draw the nose for answer 10 3.…
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type the correct answer in the box. use numbers instead of words. an ex…
-13.28
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directions: solve each problem, showing all work. then find the answer …
1. $-5$ (color purple) 2. $21$ (color yellow) 3. $60$ (color orange) 4. $12$ (color pink) 5. $-12$ (color light green) 6. $31$ (color light blue) 7. $-16$ (color dark blue) 8. $-4…
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sol review: square roots, real numbers, and interest 4028090@ccpsnet.ne…
-10 (corresponding to the option: -10)
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compute. -3.384 - 5.76 = 14.25 + (-27.381) =
$-3.384 - 5.76 = -9.144$ $14.25 + (-27.381) = -13.131$
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compute. -3.384 - 5.76 = 14.25 + (-27.381) =
$-3.384 - 5.76 = -9.144$ $14.25 + (-27.381) = -13.131$
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type the correct answer in the box. use numbers instead of words. what …
-19.527
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an expression is shown. $-\frac{1}{5} + 0.15$ which value is equivalent…
D. $-\frac{1}{20}$
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compute. -2.34 + (-6.52) = -2.8 + 45.3 =
$-2.34 + (-6.52) = -8.86$ $-2.8 + 45.3 = 42.5$
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consider the polynomial function $q(x) = 3x^4 - 5x^3 - 2x^2 + x - 18$. …
As $x$ approaches positive infinity ($x\to\infty$), $q(x)$ approaches positive infinity ($q(x)\to\infty$); as $x$ approaches negative infinity ($x\to-\infty$), $q(x)$ approaches p…
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compute. -2.34 + (-6.52) = -2.8 + 45.3 =
$-2.34 \div (-6.52) \approx 0.36$ $-2.8 \div 45.3 \approx -0.06$
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consider the polynomial function $h(x) = -7x^6 + 3x^4 - 5x^2$. what is …
As $x$ approaches positive infinity, $h(x)$ approaches negative infinity; as $x$ approaches negative infinity, $h(x)$ approaches negative infinity. Or concisely: $\text{As } x\to\…
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consider the polynomial function $h(x) = -2x^5 + 8x^4 - 2x^2 + 15$. wha…
As $x \to +\infty$, $h(x) \to -\infty$; as $x \to -\infty$, $h(x) \to +\infty$
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end behavior of polynomials google classroom microsoft teams consider t…
As $x$ approaches positive infinity, $g(x)$ approaches positive infinity; as $x$ approaches negative infinity, $g(x)$ approaches negative infinity. In notation: $\lim_{x \to +\inf…
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how can place value help me add 316 and 482? find 316 + 482. 316 = 300 …
1. For the fill-in: break apart 2. $316 + 482 = 798$ 3. Place value helps by letting you break numbers into hundreds, tens, and ones, add each place value group separately, then c…
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316 = 300 + 10 + 6 +482 = 400 + 80 + 2 700 + 90 + 8 316 + 482 = \\boxed…
798
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what is 9,000 + 600 + 70 + 11?
9681
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recall your knowledge from previous lessons. use words to describe the …
The graph of \( f(x)=(x - 1)^2 \) is the graph of \( f(x)=x^2 \) shifted 1 unit to the right. ### 2. For \( f(x) = (x + 1)^2 \)
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the figure above is the graph of the function m(t). let n(t) = m(t) + 2…
1. $n(-3)=1$ 2. $n(2)=8$ 3. $k(2.5)=6$ 4. $w(1.5)=5.5$ 5. $w(-1.5)=-0.5$ 6. $p(2)=8$
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7. for each function, state the locator point (h,k), then sketch the gr…
a. Locator point: $(-1, -3)$ b. Locator point: $(3, 4)$ c. Locator point: $(0, -3)$ --- ### Problem 8
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suppose that the dollar value ( v(t) ) of a certain house that is ( t )…
Initial value of the house: $\$320,000$ The function represents: decay Annual percent change: $23\%$ decrease
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what is 521 + 314? find the sum. first, break apart 521 into hundreds, …
First, the breakdown of 521 is: $521 = 500 + 20 + 1$ The final sum of $521 + 314$ is $835$
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multiply these fractions. cancel and simplify if necessary. 1. $1\\frac…
\(2\frac{5}{8}\) ### Problem 2: \(2\frac{1}{3} \times 5\frac{2}{5}\)
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mplete the following tables with values for the functions ( f ), ( g ) …
| $x=$ | -3 | -2 | -1 | 0 | 1 | |------|----|----|----|---|---| | $f(x)=$ | $-f(3)$ | $-f(2)$ | $-2$ | $0$ | $2$ | | $g(x)=$ | $g(3)$ | $g(2)$ | $2$ | $0$ | $2$ | | $h(x)=$ | $h(3…
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if $f(x) = x^2 + 3$, find and simplify the following: (a) $f(t + 8) =$ …
(a) $t^2+16t+67$ (b) $t^6+16t^3+67$ (c) $12$ (d) $3t^2+9$ (e) $t^4+6t^2+17$
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for the function $f(x) = 5e^x$ and $g(x) = x^3$, find the following: (a…
(a) $5e$ (b) $125e^3$ (c) $5e^{x^3}$ (d) $125e^{3x}$ (e) $5t^3e^t$
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polynomial functions and end behavior practice describe the end behavio…
1. $\lim_{x\to-\infty} g(x) = -\infty$, $\lim_{x\to\infty} g(x) = \infty$ 2. $\lim_{x\to-\infty} p(x) = \infty$, $\lim_{x\to\infty} p(x) = \infty$ 3. $\lim_{x\to-\infty} f(x) = \i…
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solve the equation using the substitution $(x - y)dx + xdy = 0$ $xdy = …
The general solution of the differential equation \((x - y)dx + xdy = 0\) is \(y = Cx-x\ln|x|\) (where \(C\) is an arbitrary constant).
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5. $f(x) = x^3 + 4x^2 - 3$ $limlimits_{x \\to -\\infty} f(x) = -\\infty…
$\lim_{x\to-\infty} f(x) = -\infty$ $\lim_{x\to\infty} f(x) = \infty$
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nction using limit notation. 2. $p(x) = 7x^4 + 3x^3 - 3x - 4$ $limlimit…
For $p(x)=7x^4+3x^3-3x-4$: $\lim_{x\to\infty} p(x) = \infty$ $\lim_{x\to-\infty} p(x) = \infty$ For $f(x)=x^3+4x^2-3$: $\lim_{x\to\infty} f(x) = \infty$ $\lim_{x\to-\infty} f(x) =…
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a laptop computer was purchased for $1600. each year since, the resale …
$y = 1600(0.73)^t$
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identify the graph of the function; y = -\\frac{2}{3}x + 5
The correct graph is the second one (top row, right of the checked incorrect graph): a line with a gentle downward slope crossing the y-axis at 5.
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the 3 points plotted below are on the graph of $y = \\log_b x$. based o…
The corresponding points to plot are $(0, 1)$, $(1, 4)$, and $(2, 16)$ (these are the points on the graph of $y=b^x$).
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5. $f(x) = x^3 + 4x^2 - 3$ $limlimits_{x \\to -\\infty} f(x) = \\infty$…
$\lim_{x\to-\infty} f(x) = -\infty$ $\lim_{x\to\infty} f(x) = \infty$
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5. which statement correctly completes the comparison below? the produc…
A. 10 times more
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consider the exponential function g where $g(x) = 6(3.2)^x$. what is th…
$y = 0$
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15. the following polynomial function is given by $f(x) = -7x^6 + 2x^2 …
(D) The sign of the leading term of $f$ is negative, and the degree of the leading term of $f$ is even; therefore, $\lim_{x \to -\infty} f(x) = -\infty$ and $\lim_{x \to \infty} f…
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3. solve. write the answer in lowest terms.. \\(\\frac{2}{5} \\times \\…
$\frac{3}{10}$
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7. determine the horizontal translation that is applied to $y = |x - 3|…
The horizontal translation is 5 units to the right (or 7 units to the right, but 5 is a more probable answer in this context). So the horizontal translation applied is \( \boldsym…
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what kind of transformation converts the graph of f(x) = -4|x| + 4 into…
vertical stretch
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evaluate the following. 6.84 + 0.28 × 0.8
$7.064$
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evaluate the following.\\(1.3 \\times 3.5 - 2.7\\)
1.85
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multiply. $-1.4\\cdot(-2)=\\square$ $-10(6.474)=\\square$
$2.8$ $-64.74$
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over which interval is the graph of ( f(x) = -x^2 + 3x + 8 ) increasing…
\( (-\infty, 1.5) \) (Option: \( (-\infty, 1.5) \))
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sketch the graph of a polynomial function that could match each stateme…
1. For $\boldsymbol{\lim_{x \to -\infty} p(x) = -\infty}$ and $\boldsymbol{\lim_{x \to \infty} p(x) = \infty}$: Sketch an odd-degree polynomial with positive leading coefficient (…
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5. which graph has a slope of one half.
The fourth graph (rightmost one) has a slope of $\frac{1}{2}$.
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for all functions of the form $f(x) = ax^2 + bx + c$, which is true whe…
The y - intercept will always be the vertex.
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13. \\(\\lim\\limits_{x\\to -\\infty} p(x) = -\\infty\\) and \\(\\lim\\…
A valid function is $\boldsymbol{p(x) = -x^2}$ (any even-degree polynomial with a negative leading coefficient is acceptable, e.g., $p(x)=-2x^4 + 3x^2 -1$ also works)
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consider the function $y = f(x)$ graphed below. the two points marked o…
$y=2\cdot2^x$ (or $y=2^{x+1}$)
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over which interval is the graph of $f(x) = \\frac{1}{2}x^2 + 5x + 6$ i…
\( (-5,\infty) \) (corresponding to the option: \( \boldsymbol{(-5,\infty)} \))
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sketch the graph of a polynomial func 12. \\(\\lim\\limits_{x\\to -\\in…
A valid graph is a straight line (or any odd-degree polynomial curve) that rises to the right, falls to the left, and is continuous with no breaks. For the simple case of $p(x)=x$…
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5 scarcity impacts opportunity costs because most resources are limited…
C. trash
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integer operations maze 2 directions: evaluate each expression. use you…
The correct path is: $-6 + 5 ightarrow -1 ightarrow -3 - (-4) ightarrow 1 ightarrow -6(-8) ightarrow 48 ightarrow -12 - (-3) ightarrow -9 ightarrow 12 + (-5) ightarrow 7 ightarrow…
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the graph of $y = x^2$ is shown on each grid in parts (a) and (b) below…
The graph of $y=(-2x)^2$ is a horizontal shrink of $y=x^2$ by a factor of $\frac{1}{2}$, passing through points like $(\frac{1}{2},1)$, $(1,4)$, $(-\frac{1}{2},1)$, $(-1,4)$, with…
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ssush15 – analyze the origins and impact of u.s. involvement in world w…
U.S. neutrality before 1917 became difficult to maintain due to trade with the Allies (intertwined economy, British blockade limiting Central Powers trade), loans to the Allies (f…
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graph the equation. $y = -6|x| + 3$
The graph is a downward-opening V with vertex at $(0, 3)$, passing through points $(-1, -3)$, $(1, -3)$, $(-0.5, 0)$, and $(0.5, 0)$, forming two linear segments: 1. For $x\geq0$:…
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17 which graph best represents the linear function $y = 2x + 2$? * 1 po…
Option 2 (the graph in Option 2) best represents the linear function \( y = 2x + 2 \).
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write a rule for g that represents a translation 3 units left and 2 uni…
$\log_{1/2}(-x+3) + 2$
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when a number is decreased by 9.8%, the result is 87. what is the origi…
96.4
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determine the slope and the y-intercept from the equation shown. * 1 po…
The correct options are: m = -1/3 b = 4
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f(t) = sin⁴(t) cos⁵(t)
$\frac{\sin^5(t)}{5} - \frac{2\sin^7(t)}{7} + \frac{\sin^9(t)}{9} + C$
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write a rule for g that represents a vertical stretch by a factor of 6,…
$g(x)=6\log_{6}x - 5$
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2. $y = x^2$
The graph is a parabola with vertex at $(0,0)$, passing through points $(-3,9), (-2,4), (-1,1), (1,1), (2,4), (3,9)$, opening upward symmetrically across the y-axis.
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y = 2x - 4 y = -x - 1 plot two lines by clicking the graph. click a lin…
To plot \( y = 2x - 4 \), use points \((0, - 4)\) and \((2,0)\). To plot \( y=-x - 1 \), use points \((0,-1)\) and \((-1,0)\). Draw lines through each pair of points.
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4. simplify: \\(\frac{sqrt{72}}{sqrt{18}}\\)
2
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write the equation of the line in fully simplified slope - intercept fo…
$y=-3x+6$
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7. a data analyst adds sharing permissions to limit who can edit the da…
A. Data security
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find the equation of the inverse. graph both equations on the same coor…
1. Inverse of \(y=2x\): \(\boldsymbol{y=\frac{x}{2}}\) - The graph of \(y=2x\) is a straight line with slope 2 passing through the origin; \(y=\frac{x}{2}\) is a straight line wit…
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each function using limit notation. 2. $p(x) = 7x^4 + 3x^3 - 3x - 4$
$\lim_{x\to+\infty} p(x) = +\infty$ and $\lim_{x\to-\infty} p(x) = +\infty$
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question 32 0.1 pts a mutual fund that is organized as a limited partne…
B. hedge fund.
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polynomial functions an describe the end behavior of each 1. ( g(x) = 4…
As $x \to +\infty$, $g(x) \to +\infty$; as $x \to -\infty$, $g(x) \to -\infty$
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supporting question 1: what types of speech are and are not protected u…
Overall, expressive clothing choices are protected by the First Amendment as free speech, with key exceptions and conditions: 1. Protection applies to symbolic speech via clothing…
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graph the function $f(x) = -2\\log_{4} x - 4$ on the axes below. you mu…
Asymptote type: Vertical; Asymptote equation: \( x = 0 \); Two points: \( (1, - 4) \), \( (4, - 6) \) (you can plot the vertical line \( x = 0 \), the point \( (1, - 4) \) and \( …
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example 6 \\(\\int \\tan^3 x \\sec x \\, dx\\)
$\frac{\sec^3 x}{3} - \sec x + C$
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graph the function $f(x) = -log_3 (x - 4)$ on the axes below. you must …
Asymptote: Vertical (and points like \( (5, 0) \) and \( (7, - 1) \) can be plotted)
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what limited contact between china and the rest of the world? powerful …
B. Physical features and distance Long distances
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graph the function $f(x) = -\\log_{5} x - 5$ on the axes below. you mus…
The asymptote is vertical (the equation of the vertical asymptote is \( x = 0 \)). Two points with integer coordinates are \( (1,-5) \) and \( (5,-6) \) (or other valid integer - …
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204 ÷ 0.6 =
340
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which decimal is equivalent to \\(\frac{5}{6}\\) ? \\(\\circ\\ 0.8\\bar…
\( 0.8\overline{3} \) (the first option: \( 0.8\overline{3} \))
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find the equation of the tangent line to the curve $y = \\frac{5x}{1 + …
$y = -\frac{30}{169}x + \frac{625}{338}$
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write the answer as a mixed number. 5 units= 11 1 unit = \\(\\frac{11}{…
$4\frac{2}{5}$
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multiplying integers find each product. 11. 2·2
4
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use the graph of the rational function in the figure shown to complete …
9. $-\infty$ 10. $+\infty$ 11. $-\infty$ 12. $+\infty$ 13. $0$ 14. $0$ 15. $+\infty$ 16. $-\infty$ 17. $-\infty$ 18. $+\infty$ 19. $1$ 20. $1$
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1. the second linear function has a slope of -4 and an x-intercept at 8…
a. The slope of the first linear function is positive, while the slope of the second linear function is negative.
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10 - 9 (vertical subtraction) and 16 - 8 (vertical subtraction)
For \( \begin{array}{r}10\\ - 9\\ \hline\end{array} \), the result is \( 1 \); for \( \begin{array}{r}16\\ - 8\\ \hline\end{array} \), the result is \( 8 \)
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non core algebra i b - cr the graph of the function ( f(x) = (x - 4)(x …
The function is decreasing for all real values of \(x\) where \(x < 1.5\).
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13 - 4; 10 - 6; 16 - 9; 12 - 6
For \( \begin{array}{r}13\\ - 4\\ \hline\end{array} \), the result is \( 9 \). For \( \begin{array}{r}10\\ - 6\\ \hline\end{array} \), the result is \( 4 \). For \( \begin{array}{…
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over which interval is the graph of $f(x) = \\frac{1}{2}x^2 + 5x + 6$ i…
B. \((-5, \infty)\)
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a. the amplitude of the function is 2. b. the maximum value of the func…
D. The midline of the function is \( y = 2 \)
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part 1: general form and components the general form of an exponential …
a) $a = 8$; It represents the initial value (the value of the function when $x=0$) b) $b = 3$; It represents the growth factor of the exponential function c) $8$ d) Growth; Becaus…
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charlemagne and his successors what positive strides did charlemagne ma…
## CHARLEMAGNE AND HIS SUCCESSORS 1. Promoted education, standardized laws, unified currency, spread Christianity. 2. Shared Christianity, Charlemagne's rule, Latin culture. 3. Re…
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9. write an exponential function with a y - intercept of 7 and a decay …
\( y = 7(0.25)^x \) ### Problem 10:
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exponential functions graphic organizer equations $y = a(b)^x$ $y = 4(\…
### EQUATIONS #### Left ($y=4(\frac{2}{3})^x$) $a=4$ $b=\frac{2}{3}$ Growth or Decay? Decay #### Right ($y=0.5(\frac{5}{2})^x$) $a=0.5$ $b=\frac{5}{2}$ Growth or Decay? Growth ###…
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2. find the slope in the table. | x | y | |----|----| | 3 | 4 | | 6 | 6…
\(\frac{2}{3}\)
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exit ticket (2.6): slope from 2 points a 1. find slope from the two poi…
\(\frac{1}{3}\)
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only a select few people can be real leaders. please select the best an…
being an inherent trait limited to a "select few". Most modern leadership frameworks reject the idea that only a small group of people can be effective leaders.
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what is the function rule for the yellow segment? f(x) = -2x + 1 f(x) =…
The function rule for the yellow segment is \( f(x) = -2x + 1 \) (the yellow box's function).
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graphing two - variable linear inequalities which linear inequality is …
\(y\geq\frac{1}{2}x + 2\) (the first option: \(y\geq\frac{1}{2}x+2\))
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the solutions to the inequality $y \\leq -x + 1$ are shaded on the grap…
B. (3, -2)