Question

Find the limit. lim  θ→0  cos(4θ) − 1 / sin(7θ)

Can't figure this out. Any help is appreciated!

Answer 1

The given limit is

`\lim_(\theta ->0)(cos(4 \theta)-1)/(sin(7 \theta))`

If we put 0 for theta , we will get 0/0 , which is not defined.

SO in this case we use L- Hospital's rule and differentiate both numerator and denominator. That is

`\lim_(\theta ->0)((d/d \theta)(cos(4 \theta)-1))/((d / d \theta)(sin(7 \theta)))`

`\lim_(\theta ->0)(-4sin(4 \theta))/(7 cos(7 \theta))`

Using substitution property of limit

`(-4sin(4 *0))/(7 cos(7*0))`

`(-4*0)/(7 *1)=0`

Therefore the value of the limit is 0.