Answered: a) limg→0 3 - Vx + 9 VE – 2 b) limz→4 Z…

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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Hi there, please help me with answering this question, I am a bit confused. Please answer all parts clearly with explanation. Also, please read the question carefully because sometimes my questions are answered incorrectly and unfortunately I do not recieve a refund for it. Please answer with legible handwritting as well. Thank you very much. Thumbs up always for correct answers! (:

6. Here are some computational problems:
a) limr→0
3 – Vr + 9
Vz - 2
b) limz→4
1
t +1
c) lim→-1
|t + 1|
y² – 4y – 21
Зу? — 17у — 28
d) limy→7

Expert Solution

A)...

$L e t I = \lim_{x \to 0} (\frac{x}{3 - \sqrt{x + 9}}) R a t i o n a l i z e t h e d e n o m i n a t o r I = \lim_{x \to 0} (\frac{x (3 + \sqrt{x + 9})}{(3 - \sqrt{x + 9}) (3 + \sqrt{x + 9})}) I = \lim_{x \to 0} (\frac{x (3 + \sqrt{x + 9})}{(3^{2} - {(\sqrt{x + 9})}^{2}}) (a^{2} - b^{2} = (a - b) (a + b)) I = \lim_{x \to 0} (\frac{x (3 + \sqrt{x + 9})}{9 - x - 9}) I = \lim_{x \to 0} (\frac{x (3 + \sqrt{x + 9})}{- x}) I = \lim_{x \to 0} (- (3 + \sqrt{x + 9})) Plug in the value x = 0 I = - 3 - \sqrt{0 + 9} I = - 3 - 3 I = - 6$