Question

determine limit: lim h->0 (4sin(h+pi/6) -2)/3h

Answer 1

Could take it to: \[\frac{ 1 }{ 3 } \times \lim h \rightarrow0 \frac{ \sin (h + \frac{ \pi }{ 6 }) - \sec \frac{\pi }{ 3 } }{ h}\]

Answer 2

left out the 4

Answer 3

you can use L'hopital's rule because if you apply the limit as it is you get 0/0 form

Answer 4

so find the derivative of the top and the derivative of the bottom and apply the limit again.

Answer 5

Ok, will give that a shot. Thanks man.

Answer 6

Note that you can rewrite the limit as:\[\frac{1}{3}\lim_{h\rightarrow 0}\left(\frac{4\sin(h+\frac{\pi}{6})-4\sin(\frac{\pi}{6})}{h}\right)\]Whats in parenthesis is the derivative of 4sin(x) when x = pi/6. Its in the form:\[\lim_{h\rightarrow 0}\frac{f(x+h)-f(x)}{h}\]with \[f(x)=4\sin(x)\] and x = pi/6.

Answer 7

Looks almost similar to differentiation from first principles.

Answer 8

which is what joe said. Thanks joe :)