Indeterminate forms 0^0 and 1^\infty. Evaluate the following limits.

xcl3411

xcl3411

Answered question

2021-11-20

Indeterminate forms 00 and 1∞. Evaluate the following limits.
a) limx→0+xx
b) limx→∞(1+1x)x

Answer & Explanation

Wasither1957

Wasither1957

Beginner2021-11-21Added 17 answers

Given to find:
a)limx→0+(x)x
b) limx→∞(1+1x)x
Part a:
Since u=eln⁡(u), then:
limx→0+xx=limx→0+eln⁡(xx)
limx→0+eln⁡(xx)=limx→0+exln⁡(x)
Move the limit under the exponential:
limx→0+exln⁡(x)=elimx→0+exln⁡(x)
elimx→0+xln⁡(x)=elimx→0+ln⁡(x)1x
Since we have an indeterminate form of type ∞∞, we can apply the LHospital
juniorekze

juniorekze

Beginner2021-11-22Added 18 answers

Part b:
Since u=eln⁡(u), then:
limx→∞(1+1x)x=limx→∞eln⁡((1+1x)x)
limx→∞eln⁡((1+1x)x)=limx→∞exln⁡(1+1x)
Move the limit under the exponential:
limx→∞exln⁡(1+1x)=elimx→∞xln⁡(1+1x)
elimx→∞xln⁡(1+1x)=elimx→∞ln⁡(1+1x)1x
Since we have an indeterminate form type 00, we can apply the LHopitals rule:
elimx→∞ln⁡(1+1x)1x=elimx→∞ddxln⁡(1+1x)ddx1x
elimx→∞ddxln⁡(1+1x)ddx1x=elimx→∞11+1x
elimx→∞11+1x=elimx→∞xx+1
elimx→∞xx+1=elimx

Do you have a similar question?

Recalculate according to your conditions!

New Questions in Calculus 1

Ask your question.
Get an expert answer.

Let our experts help you. Answer in as fast as 15 minutes.

Didn't find what you were looking for?

Product

Company

Connect with us

Get Plainmath App

Plainmath Logo

E-mail us: [email protected]

Our Service is useful for:

Plainmath is a platform aimed to help users to understand how to solve math problems by providing accumulated knowledge on different topics and accessible examples.

2023 Plainmath. All rights reserved