Mini Exam 11 — Timed Mini Exams

Questions in this quiz (10)

1. How many vertical asymptotes exist for $$f(x)=\frac{1}{2\sin^2x-\sin x-1}$$ in $$(0,2\pi)$$?

   • $$0$$
   • $$1$$
   • $$2$$
   • $$3$$

2. What value of $$k$$ will make this function continuous? $$f(x)=\begin{cases}\sin(2x),&x\le\pi\\2x+k,&x>\pi\end{cases}$$

   • $$-\pi$$
   • $$0$$
   • $$-2\pi$$
   • $$\pi$$

3. Evaluate the limit: $$\lim_{x\to0}\tan\left(\frac{1}{x}\right)$$

   • $$0$$
   • $$1$$
   • $$\infty$$
   • Does not exist

4. Approximate the slope of $$y=x^2+3$$ at $$(1,4)$$.

   • $$1$$
   • $$2$$
   • $$3$$
   • $$4$$

5. Differentiate: $$y=\frac{3}{2\sqrt[4]{x^3}}$$

   • $$\frac{9}{8x^{7/4}}$$
   • $$-\frac{3}{8x^{7/4}}$$
   • $$-\frac{9}{8x^{7/4}}$$
   • $$\frac{3}{8x^{7/4}}$$

6. Find the derivative of the volume of a sphere with respect to its radius $$r$$.

   • $$4\pi r^2$$
   • $$3\pi r^2$$
   • $$\frac{4}{3}\pi r^2$$
   • $$2\pi r$$

7. Determine the point(s) at which the graph of $$y=\frac{x-1}{x^2+3}$$ has a horizontal tangent.

   • $$x=1$$
   • $$x=-1$$
   • $$x=3,-1$$
   • $$x=0$$

8. Use the information to find $$f'(3)$$: $$g(3)=4,g'(3)=-2,h(3)=3,h'(3)=\pi$$ and $$f(x)=\frac{g(x)-h(x)}{g(x)}$$.

   • $$\frac{-2-\pi}{4}$$
   • $$\frac{-6-4\pi}{16}$$
   • $$\frac{2-\pi}{4}$$
   • $$\frac{\pi-2}{16}$$

9. A particle moves along a straight line with velocity given by $$v(t)=7-(1.01)^{-t^2}$$ at time $$t>0$$. What is the acceleration of the particle at time $$t=3$$?

   • $$-0.914$$
   • $$0.055$$
   • $$5.486$$
   • $$6.486$$

10. A balloon rises at $$15$$ feet per second from a point on the ground $$45$$ feet from an observer. Find the rate of change of the angle of elevation when the balloon is $$60$$ feet above the ground. Indicate units of measure.

    • $$\frac{3}{25}$$ rad/s
    • $$\frac{1}{5}$$ rad/s
    • $$\frac{1}{15}$$ rad/s
    • $$\frac{2}{15}$$ rad/s