33. One-sided limits Let \[ f(x)=\left\{\begin{array}{ll} x^{2}+1 & \text { if } x<-1 \\ \sqrt{x+1} & \text { if } x \geq-1 \end{array}\right. \] Compute the following limits or state that they do not exist. a. $ \lim _{x \rightarrow 1^{-}} f(x) $ b. $ \lim _{x \rightarrow-1^{-}} f(x) $ c. $ \lim _{x \rightarrow 1} f(x) $

          33. One-sided limits Let
\[
f(x)=\left\{\begin{array}{ll}
x^{2}+1 & \text { if } x<-1 \\
\sqrt{x+1} & \text { if } x \geq-1
\end{array}\right.
\]

Compute the following limits or state that they do not exist.
a. \( \lim _{x \rightarrow 1^{-}} f(x) \)
b. \( \lim _{x \rightarrow-1^{-}} f(x) \)
c. \( \lim _{x \rightarrow 1} f(x) \)

$33. One-sided limits Let f(x)={ x^2+1 if x<-1 √(x+1) if x ≥-1 . Compute the following limits or state that they do not exist. a. limx → 1^- f(x) b. limx →-1^- f(x) c. limx → 1 f(x)$

Added by Alex W.

Calculus: Early Transcendentals

William Briggs, Lyle Cochran, Bernard… 3rd Edition

Chapter 2

Instant Answer

Solved by Expert Oswaldo Jiménez

Step 1

Step 1: Understand the piecewise function $ f(x) $: \[ f(x) = \begin{cases} x^2 + 1 & \text{if } x < -1 \\ \sqrt{x + 1} & \text{if } x \geq -1 \end{cases} \] Show more…

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33. One-sided limits Let \[ f(x)=\left\{\begin{array}{ll} x^{2}+1 & \text { if } x<-1 \\ \sqrt{x+1} & \text { if } x \geq-1 \end{array}\right. \] Compute the following limits or state that they do not exist. a. $ \lim _{x \rightarrow 1^{-}} f(x) $ b. $ \lim _{x \rightarrow-1^{-}} f(x) $ c. $ \lim _{x \rightarrow 1} f(x) $