Question

Use the formal definition of limit to verify the indicated limit.

Answer 1

I understand the steps up to the red line.

Answer 2

0<x-2<d
|x+5||x-2|<E
this is as far as I can get.

Answer 3

|x+5|<8 I think

Answer 4

thats because we are assuming |x-2| < 1
so x < 3

Answer 5

ok

Answer 6

\(\large |x^2+3x-10|=|x+5|\cdot |x-2| \lt 8 \cdot \delta \)

yes ?

Answer 7

yeah because |x+5|<8

Answer 8

yes and in the start, we have \(\delta = \min(\epsilon/8, ~1)\)

Answer 9

yeah, but why does he pic that?

Answer 10

since putting \(\large \delta =1\) makes the value of \(\epsilon/8 \) greater than 1, the value of \(\large \delta \) must be \(\large \epsilon/8\) here

Answer 11

factoring |f(x) - L| must have given him that hint

Answer 12

are you able to say:
\[|x+5||x-2|<\epsilon \]
\[|x+5|<8\]
\[|x-2|<\epsilon /8\]

Answer 13

that looks good to me!

Answer 14

Ok :) thnx again

Answer 15

np :)