Can you please solve a, b, c and d Find the limit(1a) limX + 3x-3x²9Exb) lim (6x² - 6 cos x) =X->0c) limX->>0d) limX->05 COS X5+ sin x64+ex??

Answered: Find the limit a) lim ---3-9 X+ 3 b)…

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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Question

Can you please solve a, b, c and d

Find the limit
(1
a) lim
X + 3
x-3x²9
Ex
b) lim (6x² - 6 cos x) =
X->0
c) lim
X->>0
d) lim
X->0
5 COS X
5+ sin x
6
4+ex
?
?

Expert Solution

Step 1: Introduction

Given:

a) $limit as x rightwards arrow negative 3 of fraction numerator x plus 3 over denominator x squared minus 9 end fraction$

b) $limit as x rightwards arrow 0 of open parentheses 6 x squared minus 6 cos open parentheses x close parentheses close parentheses$

c) $limit as x rightwards arrow 0 of open parentheses fraction numerator 5 cos open parentheses x close parentheses over denominator 5 plus sin open parentheses x close parentheses end fraction close parentheses$

d) $limit as x rightwards arrow 0 of fraction numerator 6 over denominator 4 plus e to the power of x end fraction$

To Find:

The value of the limits.

Concept Used:

The function has a limit $L$ at an input $p$ , if $f open parentheses x close parentheses$ gets closer and closer to $L$ as $x$ moves closer and closer to $p$ .