Question

Consider the following limit.

lim (x^2 + 4)

(x--> 5)

1. Find the limit L.

2. Find the largest δ such that |f(x) − L| < 0.01 whenever 0 < |x − 5| < δ. (Assume 4 < x < 6 and δ > 0. Round your answer to four decimal places.)

I am honestly so lost... if you could please show work I would greatly appreciate it!!

Answer 1

we are given

(1)

we can plug x=5

(2)

we can plug x=5 on right side

now, we can compare with

0 < |x − 5| < δ

so, we get

............Answer