MAT 312 C.A.T II INSTRUCTIONS: Attempt all questions and clearly show your working (a) Evaluate the integral \( \int_{C} \frac{d z}{z(z-2)^{4}} \) where \( C \) is the positively oriented circle \( |z-2|=1 \).

Consider the following. \[ \begin{array}{l}y=x^{2} \\ y \\ y \\ y\end{array} \] (b) Use the integration capabilities of the graphing utility to approximate the area to four de

\( \lim _ { m \rightarrow + \infty } m [ 2 - \sin ( n ^ { 2 } + 1 ) ] \)

Ejercicio 1. Determina la derivada de cada una de las siguientes funciones. 1. \( f(x)=10^{x} \) 2. \( f(x)=14^{x}-4^{x} \) 3. \( f(x)=9^{x}+2^{x} \) 4. \( f(x)=6^{x} \) 5. \( f f(x)=\log _{6} x \) 6. \( f(x)=\log _{15} x+3 \log _{20} x-5 \log _{2} x \) 7. \( f(x)=4 \operatorname{sen} x-5 \cos x \) 8. \( f(x)=6 \tan x-6 \csc x-3 \cos x \) 9. \( f(x)=\cos x-4 \tan x \) 10. \( f(x)=4 \sec x+5 \cot x \)

Round your answers to the nearest thousandth. Do not round any intermediate computations. \[ \ln \frac{3}{4}=\square \] \( \ln 20.6=\square \)

\( \frac{d^{4} y}{d x^{4}} \mathrm{y}=\cos 2 x \) إذا كانت