Chapter 11: Q. 6 (page 901)

Finding limits: Find the given limits if they exist. If a limit does not exist, explain why.
$lim_{t \to - 3} <\frac{| t + 3 |}{t + 3}, \frac{| t + 3 |}{t - 3}>$

Short Answer

Expert verified

$lim_{t \to - 3} <\frac{| t + 3 |}{t + 3}, \frac{| t + 3 |}{t - 3}> = <1, 0>$

Step by step solution

Step 1. Given information

$lim_{t \to - 3} <\frac{| t + 3 |}{t + 3}, \frac{| t + 3 |}{t - 3}>$

Step 2. Finding limits for limt→−3 |t+3|t+3

$If \lim_{x \to a -} f (x) \neq \lim_{x \to a +} f (x) then the limit does not exist$

$lim_{x \to - 3 +} (\frac{| x + 3 |}{x + 3}) = 1$

$lim_{x \to - 3} - (\frac{| x + 3 |}{x + 3}) = - 1$

Step 3. Finding limit for limt→−3 |t+3|t-3

plug in the value

$lim_{x \to - 3} (\frac{| x + 3 |}{x - 3}) = \frac{| - 3 + 3 |}{- 3 - 3}$

$lim_{x \to - 3} (\frac{| x + 3 |}{x - 3}) = 0$

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Finding limits: Find the given limits if they exist. If a limit does not exist, explain why.
$lim_{t \to - 3} <\frac{| t + 3 |}{t + 3}, \frac{| t + 3 |}{t - 3}>$

Short Answer

Step by step solution

Step 1. Given information

Step 2. Finding limits for limt→−3 |t+3|t+3

Step 3. Finding limit for limt→−3 |t+3|t-3

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Finding limits: Find the given limits if they exist. If a limit does not exist, explain why.limt→−3 |t+3|t+3,|t+3|t−3

Short Answer

Step by step solution

Step 1. Given information

Step 2. Finding limits for limt→−3 |t+3|t+3

Step 3. Finding limit for limt→−3 |t+3|t-3

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Mechanics Maths

Probability and Statistics

Calculus

Theoretical and Mathematical Physics

Logic and Functions

Geometry

Study anywhere. Anytime. Across all devices.

Finding limits: Find the given limits if they exist. If a limit does not exist, explain why.
$lim_{t \to - 3} <\frac{| t + 3 |}{t + 3}, \frac{| t + 3 |}{t - 3}>$