Question

attempt 1: 10 attempts remaining. let ( f(x) = x^2 ). compute the value of the difference quotient ( \frac{f(5 + h) - f(5)}{h} ) when ( h = 0.04 ). round your answer to three decimal places if necessary. answer: submit answer next item

Explanation:

Step1: Find \( f(5 + h) \) and \( f(5) \)

Given \( f(x)=x^{2} \), so \( f(5 + h)=(5 + h)^{2}=25 + 10h+h^{2} \) and \( f(5)=5^{2} = 25 \).

Step2: Compute \( f(5 + h)-f(5) \)

Subtract \( f(5) \) from \( f(5 + h) \): \( f(5 + h)-f(5)=(25 + 10h+h^{2})-25=10h + h^{2} \).

Step3: Compute the difference quotient

The difference quotient is \( \frac{f(5 + h)-f(5)}{h} \), substitute \( f(5 + h)-f(5)=10h + h^{2} \) into it, we get \( \frac{10h+h^{2}}{h}=10 + h \) (for \( h
eq0 \)).

Step4: Substitute \( h = 0.04 \)

Substitute \( h = 0.04 \) into \( 10 + h \), we have \( 10+0.04 = 10.04 \).

Answer:

\( 10.04 \)