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$h(x)={[x^(2)-1," for "x <= 3],[2x+1," for "3 < x < 10]:} Find lim_(x rarr3^(-))h(x). Choose 1 answer: (A) 3 (B) 7 (C) 8 (D) The limit doesn't exist.$

\[ h(x)=\left\{\begin{array}{ll} x^{2}-1 & \text { for } x \leq 3 \\ 2 x+1 & \text { for } 3

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Math Problems

Calculus

Find derivatives of logarithmic functions

Full solution

h(x)=\left\{\begin{array}{ll} x^{2}-1 & \text { for } x \leq 3 \\ 2 x+1 & \text { for } 3<x<10 \end{array}\right.

\newline

Find

\lim _{x \rightarrow 3^{-}} h(x)

\newline

Choose

1

answer:

\newline

(A)

3

\newline

(B)

7

\newline

(C)

8

\newline

(D) The limit doesn't exist.

Step $1$ : Define the function for $x$ less than or equal to $3$ : To find the limit of $h(x)$ as $x$ approaches $3$ from the left, we need to look at the piece of the function that is defined for $x$ less than or equal to $3$ . This is the piece $x^2 - 1$ .
Step $2$ : Substitute $x = 3$ into the function: We substitute $x = 3$ into the function $x^2 - 1$ to find the limit as $x$ approaches $3$ from the left. $\newline$ $\lim_{x \to 3^{-}} h(x) = 3^2 - 1$
Step $3$ : Calculate the limit: Calculating the value gives us $9 - 1$ , which equals $8$ . $\newline$ $\lim_{x \to 3^{-}} h(x) = 8$