Theory and Examples f(x) – 5a. If lim3, find lim f(x).-2 х — 2f(x) – 5b. If limх-2 х — 24, find lim f(x).I-2

Given limx→2fx-5x-2=3. To find limx→2fx. Solving the given equation.…

Answered: f(x) – 5 a. If lim 3, find lim f(x). -2…

Calculus: Early Transcendentals

8th Edition

ISBN:9781285741550

Author:James Stewart

Publisher:James Stewart

Chapter1: Functions And Models

Section: Chapter Questions

Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...

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Theory and Examples

f(x) – 5
a. If lim
3, find lim f(x).
-2 х — 2
f(x) – 5
b. If lim
х-2 х — 2
4, find lim f(x).
I-2

Expert Solution

Step 1

Given $\lim_{x \to 2} \frac{f (x) - 5}{x - 2} = 3$ .

To find $\lim_{x \to 2} f (x)$ .

Solving the given equation.

$\begin{array}{rcl} \lim_{x \to 2} \frac{f (x) - 5}{x - 2} & = & 3 \\ \frac{\lim_{x \to 2} (f (x) - 5)}{\lim_{x \to 2} (x - 2)} & = & 3 \\ \lim_{x \to 2} (f (x) - 5) & = & 3 \lim_{x \to 2} (x - 2) \\ \lim_{x \to 2} f (x) - \lim_{x \to 2} (5) & = & 3 (2 - 2) \\ \lim_{x \to 2} \frac{f (x) - 5}{x - 2} & = & 3 \\ \frac{\lim_{x \to 2} (f (x) - 5)}{\lim_{x \to 2} (x - 2)} & = & 3 \\ \lim_{x \to 2} (f (x) - 5) & = & 3 \lim_{x \to 2} (x - 2) \\ \lim_{x \to 2} f (x) - \lim_{x \to 2} (5) & = & 3 (2 - 2) \\ \lim_{x \to 2} \frac{f (x) - 5}{x - 2} & = & 3 \\ \frac{\lim_{x \to 2} (f (x) - 5)}{\lim_{x \to 2} (x - 2)} & = & 3 \\ \lim_{x \to 2} (f (x) - 5) & = & 3 \lim_{x \to 2} (x - 2) \\ \lim_{x \to 2} f (x) - \lim_{x \to 2} (5) & = & 3 (2 - 2) \\ \lim_{x \to 2} f (x) - 5 & = & 0 \\ \lim_{x \to 2} f (x) & = & 5 \end{array}$

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