Chapter 14: Q. 19 (page 883)

In Problems 7– 42, find each limit algebraically
$\lim_{x \to 1} (5 x^{4} - 3 x^{2} + 6 x - 9)$

Short Answer

Expert verified

The value of the limit $\lim_{x \to 1} (5 x^{4} - 3 x^{2} + 6 x - 9) = - 1$

Step by step solution

Step 1. Given Information

The given limit function is $\lim_{x \to 1} (5 x^{4} - 3 x^{2} + 6 x - 9)$

We need to find the value of the limit.

Step 2. Expanding the limit

We know,

$\lim_{x \to c} [f (x) - g (x)] = \lim_{x \to c} f (x) - \lim_{x \to c} g (x)$

Therefore,

$\lim_{x \to 1} (5 x^{4} - 3 x^{2} + 6 x - 9) = \lim_{x \to 1} 5 x^{4} - \lim_{x \to 1} 3 x^{2} + \lim_{x \to 1} 6 x - \lim_{x \to 1} 9$

Step 3. Value of the limit

The simplified expression is

$\lim_{x \to 1} 5 x^{4} - \lim_{x \to 1} 3 x^{2} + \lim_{x \to 1} 6 x - \lim_{x \to 1} 9 = {5 \times {(1)}^{4}} - {3 {(1)}^{2}}} + 6 (1) - 9 = 5 - 3 + 6 - 9 = - 1$

Unlock Step-by-Step Solutions & Ace Your Exams!

Full Textbook Solutions
Get detailed explanations and key concepts
Unlimited Al creation
Al flashcards, explanations, exams and more...
Ads-free access
To over 500 millions flashcards
Money-back guarantee
We refund you if you fail your exam.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

Recommended explanations on Math Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

In Problems 7– 42, find each limit algebraically
$\lim_{x \to 1} (5 x^{4} - 3 x^{2} + 6 x - 9)$

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Expanding the limit

Step 3. Value of the limit

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Discrete Mathematics

Mechanics Maths

Geometry

Statistics

Applied Mathematics

Calculus

Study anywhere. Anytime. Across all devices.

In Problems 7– 42, find each limit algebraicallylimx→15x4-3x2+6x-9

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Expanding the limit

Step 3. Value of the limit

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Discrete Mathematics

Mechanics Maths

Geometry

Statistics

Applied Mathematics

Calculus

Study anywhere. Anytime. Across all devices.

In Problems 7– 42, find each limit algebraically
$\lim_{x \to 1} (5 x^{4} - 3 x^{2} + 6 x - 9)$