Download the App!

Get 24/7 study help with the Numerade app for iOS and Android! Enter your email for an invite.

Find the limit. Use l'Hospital's Rule where appropriate. If there is a more elementary method, consider using it. If l'Hospital's Rule doesn't apply, explain why.

$ \displaystyle \lim_{x\to 1} (2x - 1)^{\tan(\pi x/2)} $

Get the answer to your homework problem.

Try Numerade free for 7 days

Like

Report

$e^{2 / \pi}$

03:08

Wen Zheng

01:58

Amrita Bhasin

Calculus 1 / AB

Calculus 2 / BC

Chapter 4

Applications of Differentiation

Section 4

Indeterminate Forms and l'Hospital's Rule

Derivatives

Differentiation

Volume

Oregon State University

University of Michigan - Ann Arbor

Boston College

Lectures

04:35

In mathematics, the volume of a solid object is the amount of three-dimensional space enclosed by the boundaries of the object. The volume of a solid of revolution (such as a sphere or cylinder) is calculated by multiplying the area of the base by the height of the solid.

06:14

A review is a form of evaluation, analysis, and judgment of a body of work, such as a book, movie, album, play, software application, video game, or scientific research. Reviews may be used to assess the value of a resource, or to provide a summary of the content of the resource, or to judge the importance of the resource.

01:32

Find the limit. Use l'…

01:39

01:55

01:35

04:45

01:09

07:06

01:37

01:31

01:21

06:29

04:32

02:49

for this problem. We're going to be taking the limit as X goes to one of two, X minus one to the tangent kayaks over to. We're gonna want to take the natural log on both sides. So to make things a little simpler and when we do that, we're going to end up getting um the natural log of q minus X Divided by co tangent of high x over two. So now we can evaluate this at x equals one. Um but we'll get 0/0 the indeterminate form. So now we're going to use locales role. We're going to take the derivative of the numerator and we get one over to mine attacks. And then we're gonna take the derivative of asking me a negative actually. And we're going to take the derivative the denominator and we end up getting a negative coast sequence squared. Okay. Hi X over two times. Hi over two as a result of this. When we evaluate it we end up getting chew over pie. But remember that that is the natural log of Y. Yeah. Equalling two over pie. So our final answer is going to be E to the two over. Hi, for the final answer.

View More Answers From This Book

Find Another Textbook

Numerade Educator

06:12

Following are observed frequencies. The null hypothesis is HO: pl = 0.5,p2 =…

04:56

In a simple random sample of 600 voung people , 86%0 had earned high school …

04:23

In a science fair project; Emily conducted an experiment in which she tested…

08:17

Consider the area between the graphs x + 3y = 36 and x + 4 =y_ This area can…

01:30

Section 5.3 The Fundamental Theorem of Calculus: Problem 4Previous Probl…

02:03

13. If f(2) and g(*) ure clilferentiable funetions ") J)lt) dr = Lr) ex…

03:38

The velocily of particle moving back and forth on line is V =3 sin (61) …

02:19

I2 = 4 8 the graph [ f of f(c) and such 23 that%he ] [ lineta tangent to 13,…

03:35

10 sin" find the Iatal length of the curve swapt out by the point (*,&q…

02:51

Chapter 19, Review Exercises, Question 032 Use the Divergence Theorem to cal…