Question

find the limit if it exists.
\\(\lim_{x\to - 1}(10x + 9)\\)

a. (10cdot\lim_{x\to - 1}x)
b. (10cdot\lim_{x\to - 1}xcdot\lim_{x\to - 1}9)
c. (\lim_{x\to - 1}9)
d. (10cdot\lim_{x\to - 1}x+\lim_{x\to - 1}9)

select the correct choice below and, if necessary, fill in the answer box to complete your choice.

a. (\lim_{x\to - 1}(10x + 9)=) (simplify your answer.)
b. the limit does not exist.

Explanation:

Step1: Apply limit - sum rule

$\lim_{x
ightarrow - 1}(10x + 9)=10\cdot\lim_{x
ightarrow - 1}x+\lim_{x
ightarrow - 1}9$

Step2: Evaluate $\lim_{x

ightarrow - 1}x$ and $\lim_{x
ightarrow - 1}9$
We know that $\lim_{x
ightarrow a}x=a$ and $\lim_{x
ightarrow a}c = c$ (where $c$ is a constant). So, $\lim_{x
ightarrow - 1}x=-1$ and $\lim_{x
ightarrow - 1}9 = 9$.

Step3: Calculate the result

$10\cdot(-1)+9=-10 + 9=-1$

Answer:

A. $\lim_{x
ightarrow - 1}(10x + 9)=-1$