91Ó°ÊÓ

Find the area below the curve \(y=1 / \sqrt{4-x^{2}}\) from \(x--1\) to \(x=1\).

Use a graphing utility to draw the graph of \(f\) Show that \(f\) is one-to-one by consideration of \(f^{\prime}\). Draw a figure that displays both the graph of \(f\) and the graph of \(f^{-1}\). $$f(x)=4 \sin 2 x, \quad-\pi / 4 \leq x \leq \pi / 4$$

A particle moves along a coordinate line with acceleration \(a(t)=-(t+1)^{-2}\) feet per second per second. Find the distance traveled by the particle during the time interval [0,4] given that the initial velocity \(v(0)\) is 1 foot per second.

Evaluate. $$\int_{0}^{1} x 10^{1+x^{2}} d x$$

Sketch the region bounded by the curves and find its area. \(x=e^{y} . \quad y=1 . \quad y=2 . \quad x=2\).

Use a graphing utility to draw the graph of \(f\) Show that \(f\) is one-to-one by consideration of \(f^{\prime}\). Draw a figure that displays both the graph of \(f\) and the graph of \(f^{-1}\). $$f(x)=2-\cos 3 x , \quad 0 \leq x \leq \pi / 3$$

Evaluate. $$\int_{0}^{1} \frac{5 p^{\sqrt{x+1}}}{\sqrt{x+1}} d x$$

Determine the following: (i) the domain; (ii) the intervals on which \(f\) increases, decreases; (iii) the extreme values; (iv) the concavity of the graph and the points of inflection. Then sketch the graph, indicating all asymptotes. \(f(x)=(1-x) e^{x}\).

Find the ares below the curve \(y=3 /\left(9+x^{2}\right)\) from \(x=-3\) to \(x=3\).

Find a formula for the \(n\)th derivative. $$\frac{d^{n}}{d x^{n}}(\ln x)$$