Question

I need help with the limits in calculus. Problem in comments.

Answer 1

so the trick to this one is to factor the numerator and denominator: do you know how to do it?

Answer 2

Yeah I know how to do that

Answer 3

Hint: factor the denominator and see if anything cancels out

Answer 4

try factoring top and bottom as suggested
bear in mind that \(\large \bf a^2-b^2 = (a-b)(a+b)\)

Answer 5

Okay so I got\[1\div x^2+a^2\]

Answer 6

now try evaluating

Answer 7

now let x approach zero and ...what do you get?

Answer 8

1/a^2

Answer 9

Great...

Answer 10

thanks @inkyvoyd

Answer 11

no... 1/(2a^2)

Answer 12

How did you get that?

Answer 13

@inkyvoyd is correct

Answer 14

\(\Huge \lim_{x\rightarrow a}\frac{1}{x^2+a^2}\)

Answer 15

\(\Huge =\frac{1}{(a^2)+a^2}=\frac{1}{2a^2}\)

Answer 16

sorry, I said let x approach o....it should have been x approaches a...my bad

Answer 17

Why do you plug in a^2?

Answer 18

because x approaches a, not zero

Answer 19

Okay i get it now thank you guys :)