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Let $f(x) = \begin{cases} 2.7x + 11.1 & \text{if } x < -3 \\ \sqrt{x+12} & \text{if } x > -3 \\ -2 & \text{if } x = -3 \end{cases}$ Determine which one of the following rules for continuity is violated at $x = -3$. $\lim_{x \to a} f(x) = f(a)$. $\lim_{x \to a} f(x)$ exists. $f(a)$ is defined. None of the above; the function is continuous at $x = -3$. Add Work Submit Question

Name: let fx begincases 27x 111 textif x 3 sqrtx12 textif x 3 2 textif x 3 endcases determine which one of the following rules for continuity is violated at x 3 limx to a fx fa limx to a fx exis 13673
Uploaded: 2023-12-02T06:35:42-08:00
Duration: 2 min 9 s
Channel: Adi S
Description: let fx begincases 27x 111 textif x 3 sqrtx12 textif x 3 2 textif x 3 endcases determine which one of the following rules for continuity is violated at x 3 limx to a fx fa limx to a fx exis 13673

          Let $f(x) = \begin{cases} 2.7x + 11.1 & \text{if } x < -3 \\ \sqrt{x+12} & \text{if } x > -3 \\ -2 & \text{if } x = -3 \end{cases}$
Determine which one of the following rules for continuity is violated at $x = -3$.
$\lim_{x \to a} f(x) = f(a)$.
$\lim_{x \to a} f(x)$ exists.
$f(a)$ is defined.
None of the above; the function is continuous at $x = -3$.
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let fx begincases 27x 111 textif x 3 sqrtx12 textif x 3 2 textif x 3 endcases determine which one of the following rules for continuity is violated at x 3 limx to a fx fa limx to a fx exis 13673

Added by Jenny G.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Adi S

12/02/2023

Step 1

For a function $f(x)$ to be continuous at a point $x=a$, three conditions must be met: 1. $f(a)$ must be defined. 2. $\lim_{x \to a} f(x)$ must exist. This means that the left-hand limit and the right-hand limit must be equal: $\lim_{x \to a^-} f(x) = \lim_{x \to Show more…

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Let $f(x) = \begin{cases} 2.7x + 11.1 & \text{if } x < -3 \\ \sqrt{x+12} & \text{if } x > -3 \\ -2 & \text{if } x = -3 \end{cases}$ Determine which one of the following rules for continuity is violated at $x = -3$. $\lim_{x \to a} f(x) = f(a)$. $\lim_{x \to a} f(x)$ exists. $f(a)$ is defined. None of the above; the function is continuous at $x = -3$. Add Work Submit Question