Problem

Evaluate the limit and justify each step by indic…

View

Problem 8 Medium Difficulty

Evaluate the limit and justify each step by indicating the appropriate Limit Law(s).

$ \displaystyle \lim_{t \to 2}\left( \frac{t^2 - 2}{t^3 - 3t + 5} \right)^2 $

Answer

$\frac{4}{49}$

Discussion

You must be signed in to discuss.

Top Calculus 1 / AB Educators

Watch More Solved Questions in Chapter 2

Problem 1

Problem 2

Problem 3

Problem 4

Problem 5

Problem 6

Problem 7

Problem 8

Problem 9

Problem 10

Problem 11

Problem 12

Problem 13

Problem 14

Problem 15

Problem 16

Problem 17

Problem 18

Problem 19

Problem 20

Problem 21

Problem 22

Problem 23

Problem 24

Problem 25

Problem 26

Problem 27

Problem 28

Problem 29

Problem 30

Problem 31

Problem 32

Problem 33

Problem 34

Problem 35

Problem 36

Problem 37

Problem 38

Problem 39

Problem 40

Problem 41

Problem 42

Problem 43

Problem 44

Problem 45

Problem 46

Problem 47

Problem 48

Problem 49

Problem 50

Problem 51

Problem 52

Problem 53

Problem 54

Problem 55

Problem 56

Problem 57

Problem 58

Problem 59

Problem 60

Problem 61

Problem 62

Problem 63

Problem 64

Problem 65

Problem 66

Video Transcript

to evaluate this limit. We first apply the limit of a power and so from here we have limit. As T approaches two of t squared minus two over T. To the third power minus three. T plus five. All of this race too. The second power. Next you want to apply the limit of a Kocian. And so we have limit as T approaches to of T squared minus two. This all over the limit S. T approaches to of T. To the third power minus three. T plus five. This race too, the second power. And then from here we apply limit of assam or difference. And so we have the square of the limit as T approaches two of T squared minus limit as T Approaches two of 2. This all over limit as T approaches to of T Q minus limit as T approaches to of three T plus limit as T approaches two of five. And then from here we apply limit of a constant and so we simplify this to the square of limit as T approaches to of T squared minus two over have limits S. D. Approaches to of T. To the third power minus limit as T approaches to of three T plus five. And then we apply limit of a power and so we have the square of limits As he approaches to of tea and then Square -2. All over. You have limit as T approaches to of T. And then Raised to the 3rd power minus three limit as the approaches to of T. And then plus five. And so we have two squared minus two over. Due to the 3rd power minus three times 2 plus five squared we have two over eight minus six plus five and then squared we have the square of 2/7 or that's four over 49. And so this is the value of the limits.

Ma. Theresa A.

Other Schools

Topics

Limits

Derivatives

Calculus: Early Transcendentals

Chapter 2

Limits and Derivatives

Section 3

Calculating Limits Using the Limit Laws

Problem