lim sin(2x)/tanx , x-->0
I'm not sure if I'm doing this right, I've never used one of these before...hopefully I'm posting this in the right spot.
Anyways, I can't seem to figure this question out...any help would be much appreciated!! Thanks
lim sin(2x)/tanx , x-->0
I'm not sure if I'm doing this right, I've never used one of these before...hopefully I'm posting this in the right spot.
Anyways, I can't seem to figure this question out...any help would be much appreciated!! Thanks
Two identities are used:
- $\displaystyle \sin (2\theta) = 2\sin \theta \cos \theta$
- $\displaystyle \tan \theta = \frac{\sin \theta}{\cos \theta}$
So:
$\displaystyle \lim_{x \to 0} \frac{\sin 2x}{\tan x} = \lim_{x \to 0} \frac{\ 2\sin x \cos x \ }{\displaystyle \frac{\sin x}{\cos x}}$
Then do some algebra (dividing fractions is the same thing as multiplying the numerator by the reciprocal of the denominator):
$\displaystyle = \lim_{x \to 0 } 2\sin x \cos x \cdot \frac{\cos x}{\sin x}$
Things cancel and you should be good.
Not if you know that to divide by a fraction, you "invert and multiply"!
$\displaystyle \frac{a}{\frac{b}{c}}= a\left(\frac{c}{b}\right)= \frac{ac}{b}$
Do you understand that?
When James Bond said he couldn't explain it better, he had already said that:
"Then do some algebra (dividing fractions is the same thing as multiplying the numerator by the reciprocal of the denominator):"