How Do You Estimate the Slope of a Tangent to y=2^x at (0,1)?

[fstam2]

Hey there, I need a little push in the right direction.
Here is the question:
The slope of the tangent line to the graph of the exponential function
y=2^x at the point (0,1) is lim x approaches 0 (2^x-1)/x.
Estimate the slope to three decimal places.
Where I am getting confused is which formula do I plug (x) into to find a secant slope?
I hope I asked the right question.
Thanks

 

[HallsofIvy]

Hey there, I need a little push in the right direction.
Here is the question:
The slope of the tangent line to the graph of the exponential function
y=2^x at the point (0,1) is lim x approaches 0 (2^x-1)/x.
Estimate the slope to three decimal places.
Where I am getting confused is which formula do I plug (x) into to find a secant slope?
I hope I asked the right question.
Thanks

Yes, since you are only asked to "estimate the slope to three decimal places" you just need to plug a small enough x into that secant formula which is exactly what you wrote: (2^x-1)/x. That should take about 5 seconds using a calculator!

(Finding the limit itself in order to find the actual formula is much harder!)

 

[fstam2]

Thank you for your help