Can you help me? II. Find each of the following limits. Show work.2х-1limx->5x -7x+10211-x6. limCOSX5.

Name: Can you help me? II. Find each of the following limits. Show work.2х-
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Description: Can you help me? II. Find each of the following limits. Show work.2х-1limx->5x -7x+10211-x6. limCOSX5.

Given : limx→52x-1x2-7x+10 limx→π2 1-xcosx

Answered: II. Find each of the following limits.…

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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Can you help me?

II. Find each of the following limits. Show work.
2х-1
lim
x->5x -7x+10
21
1-x
6. lim
COSX
5.

Expert Solution

Step 1

Given :

$\lim_{x \to 5} (\frac{(2 x - 1)}{(x^{2} - 7 x + 10)})$

$\lim_{x \to \frac{π}{2}} (\frac{1 - x}{\cos x})$

Step 2

We have to find limit.

$\lim_{x \to 5} (\frac{(2 x - 1)}{(x^{2} - 7 x + 10)})$

$\lim_{x \to 5^{-}} (\frac{(2 x - 1)}{(x^{2} - 7 x + 10)}) = \lim_{x \to 5^{-}} (2 x - 1) {(x^{2} - 7 x + 10)}^{- 1} = (2 (5) - 1) {({(5)}^{2} - 7 (5) + 10)}^{- 1} = 9 (- \infty) = - \infty \lim_{x \to 5^{-}} (\frac{(2 x - 1)}{(x^{2} - 7 x + 10)}) = - \infty$

$\lim_{x \to 5^{+}} (\frac{(2 x - 1)}{(x^{2} - 7 x + 10)}) = \lim_{x \to 5^{+}} (2 x - 1) {(x^{2} - 7 x + 10)}^{- 1} = (2 (5) - 1) {({(5)}^{2} - 7 (5) + 10)}^{- 1} = 9 (\infty) = \infty \lim_{x \to 5^{+}} (\frac{(2 x - 1)}{(x^{2} - 7 x + 10)}) = \infty$

since the corresponding one-sided limits are not equal.

Therefore limit does not exist.

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