Q. 11 Let m(x)=Axr聽be a power functio... [FREE SOLUTION]

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Chapter 7: Q. 11 (page 639)

Let $m (x) = A x^{r}$ be a power function. Evaluate $\lim_{x 鈫� 鈭�} m (x)^{1 / x}$ .

Short Answer

Expert verified

The value is $1 .$

Step by step solution

Step 1. Given information.

We are given $\lim_{x 鈫� 鈭�} m (x)^{1 / x}$ .

Step 2. Value of the limit.

We can write,

$\lim_{x 鈫� 鈭�} m (x)^{\frac{1}{x}} m (x)^{\frac{1}{x}} = \lim_{x 鈫� 鈭�} {(A x^{r})}^{\frac{1}{x}} \lim_{x 鈫� 鈭�} {(A x^{r})}^{\frac{1}{x}} = \lim_{x 鈫� 鈭�} (A)^{\frac{1}{x}} \lim_{x 鈫� 鈭�} {(x^{y})}^{\frac{1}{x}} = \lim_{x 鈫� 鈭�} (A)^{\frac{1}{x}} \lim_{x 鈫� 鈭�} (x^{\frac{r}{x}}) N o w, a^{x} = e^{\ln (a^{x})} x^{\frac{r}{x}} = e^{\ln (x^{\frac{t}{x}})} = e^{\frac{r}{x} \ln (x)} \lim_{x 鈫� 鈭�} (x^{\frac{r}{x}}) = \lim_{x 鈫� 鈭�} e^{\frac{r}{x} \ln (x)} = e^{\lim_{x 鈫� 鈭�} (\frac{r}{x} \ln (x))} = 1 T h e r e f o r e, \lim_{x 鈫� 鈭�} {(A x^{r})}^{\frac{1}{x}} = 1 \lim_{x 鈫� 鈭�} m (x)^{\frac{1}{x}} = 1$

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91影视

Let $m (x) = A x^{r}$ be a power function. Evaluate $\lim_{x 鈫� 鈭�} m (x)^{1 / x}$ .

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Value of the limit.

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91影视

Let m(x)=Axrbe a power function. Evaluatelimx鈫�鈭�m(x)1/x.

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Value of the limit.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Mechanics Maths

Calculus

Discrete Mathematics

Probability and Statistics

Pure Maths

Theoretical and Mathematical Physics

Study anywhere. Anytime. Across all devices.

Let $m (x) = A x^{r}$ be a power function. Evaluate $\lim_{x 鈫� 鈭�} m (x)^{1 / x}$ .