the sl0pe of the tangent line to the graph of the exponential function y=2^x at the point (0,1) is

Question

lim(x->0)(2^x-1)/x.
estimate the slope of three decimal places.

f'(x)=2^x. what do i do. we have to solve this without using derivative. i keep getting zero.

Answer 1

you have the derivative wrong.

f'(x)= 2^x * ln2

But you cant use derivatives...Can you use L'Hopitals Rule for limits of the form 0/0 ?

If so, then the limit becomes

slope= (2^x ln2 -0)/1 and as x>0, this is ln 2.