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Limits

Find the limit

lim 3e^2x - 3
x→0 ¯¯¯¯x¯¯¯¯

by recognizing it as a derivative f'(a) of the appropriate function at a suitable value of a. Please specify the function f in the answer - numerical computation of the limit is not enough.

(^ means exponent and 3e^2x - 3 is over x)

Solution Preview

f(x) = 3e^2x
f(0) = 1

lim 3e^2x - 3
x→0 ¯¯¯¯x¯¯¯¯ =

= lim f(x) - f(0)
x→0 ¯¯¯¯x¯- 0¯¯¯

Let assume:

u = 2x
x ...

$2.19