please any body help me
For #3, I'd try the ratio test. It works well with factorials and powers.
For #1, can you find the derivative of $\displaystyle 3^{sin({\theta})}$?.
Try logarithmic differentiation.
I'll use x instead of theta for the sake of typing.
$\displaystyle y=3^{sin(x)}$
$\displaystyle ln(y)=ln(3^{sin(x)})$
$\displaystyle ln(y)=sin(x)ln(3)$
Differentiate:
$\displaystyle \frac{y'}{y}=cos(x)ln(3)$
Remember, $\displaystyle y=3^{sin(x)}$
$\displaystyle y'=cos(x)3^{sin(x)}ln(3)$