Question

Limits

Answer 1

(Sorry, internet's slow)

Answer 2

I don't understand how the answer is "0".

Answer 3

1-cos^2 = sin^2

lim of sin(x) sin(x)/x is?

Answer 4

*sin(x)^2/x

Answer 5

if x to 0, then sin(x)/x limits to 1

sin(x) all by itslef limits to 0

Answer 6

yes, sin^2(x)/x = sin(x) * sin(x)/x

Answer 7

or by laplace

sin^2 derives to 2sincos or sin(2x)
and x to 1

Answer 8

not sure what methods are avalibale to you

Answer 9

So x becomes 1?

I'm not well versed in calc yet; I just started like a few weeks ago but thanks for helping me, seriously

Answer 10

you should have a ...squeeze thrm which they use to make you memorize sin(x)/x

also, isnt the limit of a product the product of the limits?

Answer 11

l(ab) = l(a) * l(b) ?? i forget those rules

Answer 12

Yeah, and there's a quotient rule too. So could I apply the quotient rule here? Because I just tried it and it gave me 0

Answer 13

sin(x) = x + x^3 + x^5 + ... or some variation

sin(x)/x = 1 + x^2 + x^4 + ..., when x=0 all cancel but 1

lim (x to 0) sin(x)/x = 1

Answer 14

soo .... sin(0) = 0 so that gives us 0*1 = 0 in my defense :)

Answer 15

That makes so much more sense that what I was finding elsewhere! Thanks for everything

Answer 16

good luck