basic limit question

ming2194

1. The problem statement, all variables and given/known data



2. Relevant equations
above


3. The attempt at a solution

1st part should be okay for me and my ans is e^(2c)

for the 2nd part, i have tried to use f'(x)=lim h-->infinity f(x+h)-f(x) / h and that just prove f'(x)=e but i found it maybe useless for finding c. so any hints can give me??

or may i treat right side of the inquality as lim x--> infinity f(x) - lim x--> infinity f(x-1) ?

thx

LumenPlacidum

Look at the right hand side of your second part. Notice that it's

limit as x gets large of: ( f(x) - f(x-1) ) / ( x - (x-1))

If the actual derivatives of f are approaching a slope of e as x gets large, then what do you suppose is happening to slopes of secants measured way out there where x is very large?

ming2194

soory i cant get what you mean. may be it is too theoretic for me..

LumenPlacidum

Well, what is the form for the slope of a secant line to the graph of a function? How does that relate to the slope of the tangent line at some point?

ming2194

delete

thx

LumenPlacidum

Well done!