Consider the function h(x)=e^x. Determine the equation for the tangent line at x = 1. All values must be exact (no decimal values)

Answer 1

the slope for any x is
h'(x) = e^x
So, at the point (1,e) the slope is e
That means the equation of the line is
y-e = e(x-1)

See the graphs at

https://www.wolframalpha.com/input/?i=plot+y%3De%5Ex,+y%3Dex