Chapter 3: Q. 91 (page 312)

Use L’Hopital’s rule to prove that every exponential growth function dominates the power function $g (x) = x^{2}$

Short Answer

Expert verified

Every exponential growth function dominates the power function

Step by step solution

Step 1. Given information

The given function is $g (x) = x^{2}$

Step 2. Evaluate the values

Evaluate $f (x) a n d g (x)$

$\lim_{x \to \infty} f (x) = \lim_{x \to \infty} A e^{k x} = A e^{k (\infty)} = \infty \lim_{x \to \infty} g (x) = \lim_{x \to \infty} x^{2} = \infty^{2} = \infty$

$\lim_{x \to \infty} \frac{f (x)}{g (x)} = \lim_{x \to \infty} \frac{A e^{k x}}{x^{2}} = \lim_{x \to \infty} \frac{A k^{2} e^{k x}}{2} = \infty$

Step 3. The solution

Every exponential growth function dominates the power function

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Use L’Hopital’s rule to prove that every exponential growth function dominates the power function $g (x) = x^{2}$

Short Answer

Step by step solution

Step 1. Given information

Step 2. Evaluate the values

Step 3. The solution

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Use L’Hopital’s rule to prove that every exponential growth function dominates the power functiongx=x2

Short Answer

Step by step solution

Step 1. Given information

Step 2. Evaluate the values

Step 3. The solution

One App. One Place for Learning.

Most popular questions from this chapter

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Use L’Hopital’s rule to prove that every exponential growth function dominates the power function $g (x) = x^{2}$