Chapter 14: Q. 20 (page 883)

In Problems 7– 42, find each limit algebraically
$\lim_{x \to - 1} (8 x^{5} - 7 x^{3} + 8 x^{2} + x - 4)$

Short Answer

Expert verified

The value of the limit is $2$

Step by step solution

Step 1. Given Information

The given limit is $\lim_{x \to - 1} (8 x^{5} - 7 x^{3} + 8 x^{2} + x - 4)$

We need to find the value of the limit.

Step 2. Expanding the limit

We know,

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

Therefore,

$\lim_{x \to - 1} (8 x^{5} - 7 x^{3} + 8 x^{2} + x - 4) = \lim_{x \to - 1} 8 x^{5} - \lim_{x \to - 1} 7 x^{3} + \lim_{x \to - 1} 8 x^{2} + \lim_{x \to - 1} x - \lim_{x \to - 1} 4 = 8 \cdot \lim_{x \to - 1} x^{5} - 7 \cdot \lim_{x \to - 1} x^{3} + 8 \cdot \lim_{x \to - 1} x^{2} + \lim_{x \to - 1} x - \lim_{x \to - 1} 4$

Step 3. Substitution of limit

The simplified expression will be

= 8 \cdot \lim_{x \to - 1} x^{5} - 7 \cdot \lim_{x \to - 1} x^{3} + 8 \cdot \lim_{x \to - 1} x^{2} + \lim_{x \to - 1} x - \lim_{x \to - 1} 4 = 8 \cdot (- 1)^{5} - 7 \cdot (- 1)^{3} + 8 \cdot (- 1)^{2} + (- 1) - 4 = - 8 + 7 + 8 - 1 - 4 = 2

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In Problems 7– 42, find each limit algebraically
$\lim_{x \to - 1} (8 x^{5} - 7 x^{3} + 8 x^{2} + x - 4)$

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Expanding the limit

Step 3. Substitution of limit

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In Problems 7– 42, find each limit algebraicallylimx→-18x5-7x3+8x2+x-4

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Expanding the limit

Step 3. Substitution of limit

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Statistics

Geometry

Discrete Mathematics

Pure Maths

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Mechanics Maths

Study anywhere. Anytime. Across all devices.

In Problems 7– 42, find each limit algebraically
$\lim_{x \to - 1} (8 x^{5} - 7 x^{3} + 8 x^{2} + x - 4)$