1-6 Write the composite function in the form \( f(g(x)) \). \( [ \) Identify the inner function \( u=g(x) \) and the outer function \( y=f(u) \). Then find the derivative \( d y / d x \) \( \begin{array}{ll}\text { 1. } y=\left(5-x^{4}\right)^{3} & \text { 2. } y=\sqrt{x^{3}+2} \\ \text { 3. } y=\sin (\cos x) & \text { 4. } y=\tan \left(x^{2}\right)\end{array} \)

\( e^{(4+i)x} \)

(a) \( \sum_{n=1}^{\infty} 2\left(\frac{4}{3}\right)^{n-1} \)

Suppose \( \int_{2}^{4} f(x) d x=-8 \int_{2}^{7} f(x) d x=6 \), and \( \int_{2}^{7} g(x) d x=5 \). Evaluate the following integrals. \( \int_{2}^{7} 6 g(x) d x=30 \) \( \int_{2}^{7}[g(x)-f(x)] d x=-1 \) (Simplify your answer) (Simplify your answer) \( \int_{2}^{7}[5 g(x)-f(x)] d x=\square \) (Simplify your answer.)

\( \int_{0}^{5} f(x) d x \), where \( f(x)=\left\{\begin{array}{ll}5 & \text { if } x \leq 3 \\ 3 x-4 & \text { if } x>3\end{array}\right. \)

Complete the following steps for the given function interval, and value of \( n \). a. Sketch the graph of the function on the given interval. b. Calculate \( \Delta x \) and the grid points \( x_{0} x_{1} \quad x_{n} \) c. Illustrate the left and right Riemann sums, and determine which Riemann sum underestimates and which sum overestimates the area under the curve d. Calculate the left and right Riemann sums. \[ f(x)=\cos (x-5 \pi / 8) \text { on }[\pi / 2 \pi] n=4 \]