Chapter 3: Q. 90 (page 312)

In your own words, prove the special case of L’Hopital’s ˆ
rule that is proved in the reading. Explain each step in
detail.

Short Answer

Expert verified

The special case of L’Hopital’s ˆ rule is proved

Step by step solution

Step 1. Given information

To prove the special case of L’Hopital’s ˆ rule

Step 2. Prove the special case

$\lim_{x \to a} \frac{f (x)}{g (x)} = \lim_{x \to a} \frac{\frac{f (x) - f (a)}{x - a} \cdot (x - a) + f (a)}{\frac{g (x) - g (a)}{x - a} \cdot (x - a) + g (a)} = \lim_{x \to a} \frac{\frac{f (x) - f (a)}{x - a} . (x - a) + 0}{\frac{g (x) - g (a)}{x - a} \cdot (x - a) + 0} = \lim_{x \to a} \frac{λ - υ}{\frac{g (x) - g (a)}{x - a}} = \frac{f' (a)}{g' (a)} = \frac{\lim_{x \to a} f' (x)}{\lim_{x \to a} g' (x)}$

Step 3. The solution

The special case of L’Hopital’s ˆ rule is proved

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In your own words, prove the special case of L’Hopital’s ˆ
rule that is proved in the reading. Explain each step in
detail.

Short Answer

Step by step solution

Step 1. Given information

Step 2. Prove the special case

Step 3. The solution

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In your own words, prove the special case of L’Hopital’s ˆrule that is proved in the reading. Explain each step indetail.

Short Answer

Step by step solution

Step 1. Given information

Step 2. Prove the special case

Step 3. The solution

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Pure Maths

Theoretical and Mathematical Physics

Decision Maths

Logic and Functions

Geometry

Calculus

Study anywhere. Anytime. Across all devices.

In your own words, prove the special case of L’Hopital’s ˆ
rule that is proved in the reading. Explain each step in
detail.