Prove limit of function by using definition (delta-epsilon)

Question

asked Apr 18, 2024 30.7k views

1 Answer

Selkie · Answer 1 · 2024-04-24T03:09:32+0000

Answer:

Refer to step-by-step

Explanation:

Prove the following,
$\lim_(x \to \ 2) 2^(x)=4$ ,
$\lim_(z \to \ -1) 3^(x)=(1)/(3)$ , and
$\lim_(x \to \ 1) e^(x-1) = 1$ .

For part f:

Plug in the value of the limit, 2,

(2)^(2) =4

Thus we proved the limit.

For part g:

Plug in the value of the limit, -1,

3^((-1)) =>
3^(-1) =>
(1)/(3^(1) )=(1)/(3)

Thus we proved the limit.

For part h:

Plug in the value of the limit, 1,

e^((1)-1) =>
e^(1-1) =>
e^(0)=1

Thus we proved the limit.