Question

evaluate the limit 1. as x approaches 0 , (3x^2-x-2)/(7x^2+5x-1)
2. as x approaches 0 (tanx-sinx)/x^3

Answer 1

for the first one i got 2 but i'm not sure of the answer

Answer 2

well you are write since (3(0)^2-0-2)=-2
and (7(0)^2)+5(0)-1)=-1
and -2/-1 is 2

Answer 3

right *

Answer 4

okay , i got the first right.

Answer 5

The next one isn't as simple because you cannot just plug in 0.

Answer 6

because you get 0/0

Answer 7

0/0 means you have more work to do

Answer 8

do you know l'hopital's rule?

Answer 9

yes

Answer 10

that is differentiating the numerator and the denominator

Answer 11

yep

Answer 12

wiii it be\[\frac{ \sec ^{2}x-cosx }{ 3x ^{2} }\]

Answer 13

yes but what happens when you plug in 0?

Answer 14

it will still give 0/0

Answer 15

so do l'hoptal again

Answer 16

if we keep differentiating a polynomial we will eventually get a constant so don't worry
this has a send

Answer 17

this will end*

Answer 18

this has a end it what I meant

Answer 19

okay

Answer 20

so i have to keep on differentiating until i get a constant

Answer 21

well you can keep on using l'hoptal if you have the 0/0
eventually you won't have that because eventually the bottom will be equal to a constant that isn't 0