Use a linear approximation (or differentials) to estimate the given number.

Question

e0.01

Answer 1

y = e^x
y' = e^x
at x=1, y=1
The line through (0,1) with slope=1 is
y = x+1

so, e^0.01 ~ 1+0.01 = 1.01

Note that e^x = 1 + x + 1/2 x^2 + ...
so as a line, e^x ~ 1+x near x=0.

Answer 2

Kela, 8 consecutive questions without any indication on your part to show us where your problem is.
Please show us some effort and steps so we can see where you are having problems.

As it stands it looks like a typical case of "homework dumping"