Show that the indeterminate forms and do not always have a value of 1 by evaluating each

Chapter 8, Problem 119

(choose chapter or problem)

Indeterminate Forms Show that the indeterminate forms \(0^{0}\), \(\infty^{0}, \text { and } 1^{\infty}\) do not always have a value of 1 by evaluating each limit.

(a) \(\lim _{x \rightarrow 0^{+}} x^{\ln 2 /(1+\ln x)}\)

(b) \(\lim _{x \rightarrow \infty} x^{\ln 2 /(1+\ln x)}\)

(c) \(\lim _{x \rightarrow 0}(x+1)^{(\ln 2) / x}\)

Text Transcription:

0^0

infty^0

1^infty

lim _x rightarrow 0^+x^ln 2 1+\ln x

lim _x rightarrow infty x^ln 2 1+ln x

lim _x rightarrow 0 x+1^ln 2 x

Unfortunately, we don't have that question answered yet. But you can get it answered in just 5 hours by Logging in or Becoming a subscriber.

Becoming a subscriber
Or look for another answer

×

Login

Login or Sign up for access to all of our study tools and educational content!

Forgot password?
Register Now

×

Register

Sign up for access to all content on our site!

Or login if you already have an account

×

Reset password

If you have an active account we’ll send you an e-mail for password recovery

Or login if you have your password back