Could you please calculate this limit : `lim_(x->0) (2^(2x) + 2*2^x - 3)/(2^x - 1)`

Expert Answers

An illustration of the letter 'A' in a speech bubbles

The limit `lim_(x->0) (2^(2x) + 2*2^x - 3)/(2^x - 1)` has to be determined.

`lim_(x->0) (2^(2x) + 2*2^x - 3)/(2^x - 1)`

`= lim_(x->0) (2^(2x) + 3*2^x - 2^x - 3)/(2^x - 1)`

`= lim_(x->0) (2^x(2^x + 3) - 1(2^x + 3))/(2^x - 1)`

`= lim_(x->0) ((2^x - 1)(2^x + 3))/(2^x - 1)`

`= lim_(x->0) (2^x + 3)`

Substitute x = 0

=> 1 + 3 = 4

The limit `lim_(x->0) (2^(2x) + 2*2^x - 3)/(2^x - 1) = 4`

Approved by eNotes Editorial Team

We’ll help your grades soar

Start your 48-hour free trial and unlock all the summaries, Q&A, and analyses you need to get better grades now.

  • 30,000+ book summaries
  • 20% study tools discount
  • Ad-free content
  • PDF downloads
  • 300,000+ answers
  • 5-star customer support
Start your 48-Hour Free Trial