d) \( f(x)=-\frac{3}{s^{2}}-\frac{4}{s^{4}} \) a. \( 6 s^{-3}+16 s^{-5} \) b. \( 16 x^{4}+2 x \)

7. Find \( \lim _{x \rightarrow 2} \frac{\sqrt{6-x}-2}{\sqrt{3-x}-1} \) 8. If \( f(x)=x^{2}+10 \sin x \), show that there is a number \( c \) such that \( f(x)=1000 \)

USing first principle prove that \( y=\sin x \) then \( \frac{d y}{d x}=\cos x \)

By using Newton-Raphson Method, determine the root for \( x^{3}+2 x^{2}-1=0 \). Given \( x_{0}=0.5 \). Give the answer correct to four decimal places. Dengan mengomenan

Calcule \( \int \frac{x^{4} - 5x^{2} + 6}{x-2} \,dx \) aplicando o método de divisão longa.

integral \( \int_{0}^{1} \int_{e^{y}}^{e} \frac{x}{\ln x} d x d y \) (by