Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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Question
![**Evaluate the limit.**
\[
\lim_{{x \to 0}} (1 - 5x)^{1/x}
\]
This problem asks you to evaluate the limit of the expression \((1 - 5x)^{1/x}\) as \(x\) approaches 0. To solve this, you might consider using techniques such as L'Hôpital's Rule or the natural logarithm to simplify the expression. The final answer will help in understanding the behavior of exponential expressions as their variables approach certain critical values.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ffb4562d2-ab10-49bf-b0aa-7e3eca82fcb1%2F986a32ec-35bc-465e-931a-1f3b8f986550%2Fyg38xg2_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Evaluate the limit.**
\[
\lim_{{x \to 0}} (1 - 5x)^{1/x}
\]
This problem asks you to evaluate the limit of the expression \((1 - 5x)^{1/x}\) as \(x\) approaches 0. To solve this, you might consider using techniques such as L'Hôpital's Rule or the natural logarithm to simplify the expression. The final answer will help in understanding the behavior of exponential expressions as their variables approach certain critical values.
Expert Solution
Step 1
Given , limx->0 (1-5x)1/x
Putting x = 0 ,
=> = ( 1 - 5*0)1/0 = 1
As f(0) is in the form of 1 and in the form f(x)g(x) , Hence we will use
=> limx->0 eg(x) { f(x) - 1 } to solve the limit ,
Step 2
So, solution of given limit function ,
=> limx->0 e(1/x){(1-5x )- 1} = limx->0 e(1/x){-5x}
=> limx->0 e(-5) = e-5 =(1/e5)
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