Question

3. Consider the function: $f(x) = \begin{cases} x+1 & \text{if } x < -1 \\ x^2 & \text{if } -1 \leq x \leq 1 \\ \sqrt{x} & \text{if } x > 1 \end{cases}$ Find the following limits, if they exit. a) $\lim_{x \to -1} f(t)$ b) $\lim_{x \to 0} f(t)$ c) $\lim_{x \to 1} f(t)$

Name: 3 consider the function fx begincases x1 textif x 1 x2 textif 1 leq x leq 1 sqrtx textif x 1 endcases find the following limits if they exit a limx to 1 ft b limx to 0 ft c limx to 1 ft 94285
Uploaded: 2020-05-28T09:27:30-08:00
Duration: 1 min 4 s
Channel: Amy Jiang
Description: 3 consider the function fx begincases x1 textif x 1 x2 textif 1 leq x leq 1 sqrtx textif x 1 endcases find the following limits if they exit a limx to 1 ft b limx to 0 ft c limx to 1 ft 94285

          3. Consider the function:
$f(x) = \begin{cases} x+1 & \text{if } x < -1 \\ x^2 & \text{if } -1 \leq x \leq 1 \\ \sqrt{x} & \text{if } x > 1 \end{cases}$
Find the following limits, if they exit.
a) $\lim_{x \to -1} f(t)$
b) $\lim_{x \to 0} f(t)$
c) $\lim_{x \to 1} f(t)$

3 consider the function fx begincases x1 textif x 1 x2 textif 1 leq x leq 1 sqrtx textif x 1 endcases find the following limits if they exit a limx to 1 ft b limx to 0 ft c limx to 1 ft 94285

Added by Michelle M.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Amy Jiang

05/28/2020

Step 1

If they are equal, the limit exists and is equal to that value. For part a) $\lim_{x \to -1} f(t)$: We need to consider the function definition around $x = -1$. For $x < -1$, $f(x) = x+1$. For $x \geq -1$, $f(x) = x^2$ (specifically for $-1 \leq x \leq 1$). Step Show more…

Show all steps

Thanks for your feedback!

3. Consider the function: $f(x) = \begin{cases} x+1 & \text{if } x < -1 \\ x^2 & \text{if } -1 \leq x \leq 1 \\ \sqrt{x} & \text{if } x > 1 \end{cases}$ Find the following limits, if they exit. a) $\lim_{x \to -1} f(t)$ b) $\lim_{x \to 0} f(t)$ c) $\lim_{x \to 1} f(t)$