Find functions \( f \) and \( g \) so that \( f \circ g=H \). \( H(x)=(7 x+1)^{6} \) \( \begin{array}{ll}\text { A. } \\ f(x)=x^{6}, g(x)=7 x+1 & f(x)=7 x+1, g(x)=x^{6} \\ \text { Choose the correct pair of functions. } & \text { B. } \\ f(x)=\frac{x-1}{7}, g(x)=\sqrt[6]{x} & f(x)=\sqrt[6]{x}, g(x)=\frac{x-1}{7}\end{array} \)

For each problem, approximate the area under the given function and above the \( x \)-axis on the give interval using the specified number of rectangles/trapezoids. You may use your calculator. 1.) \( f(x)=x^{2}-3 x+4,[1,4], n=6 \) a) Left Rectangles b) Right Rectangles c) Midpoint Rectangles d) Trapezoids

Evaluate the integral. \( \int_{0}^{1} \sin (3 \pi t) d t \)

Quelle estla dérivée de la fonction \( f \) ? Wh admettra qu'elle est dérivable sur chaque intervalle contenu dans son domaine de définition \( D=\mathbb{R} \) \[ f: x \mapsto \frac{1}{e^{x}+7} \]

For each problem, approximate the area under the given function and above the \( x \)-axis on the given interval using the specified number of rectangles/trapezoids. You may use your calculator. 1.) \( f(x)=x^{2}-3 x+4,[1,4], n=6 \) a) Left Rectangles b) Right Rectangles c) Midpoint Rectangles d) Trapezoids (a)

- \( \int x \cos x d x=u \cdot v-\int v d u \)