Question

Find the limit.

Answer 1

?

Answer 2

\[\lim_{h \rightarrow 0}\frac{ \sin (x+h) - \sin (x) }{ h }\]
It comes out as cos(x) but I don't know how.

Answer 3

use the property that sin(A+B) = sin A cos B +cos A sinB
so whats sin (x+h) = ... ?

Answer 4

sin(x)cos(h)+cos(x)sin(h)

Answer 5

that - sin x
then factor out sin x from the 2 terms of numerator

Answer 6

sinx(cos(h)-1)+cos(x)sin(h)

Answer 7

right, now distribute the 'h' in the denominator to both these terms

sinx(cos(h)-1)/h +cos(x)sin(h)/h

can you find the limit to these terms individually ?

Answer 8

0+cos(x)(1) which means that it's cos(x)....OH!

Answer 9

yes! :)

Answer 10

Thanks Hartnn for guiding me :D

Answer 11

you are most welcome ^_^