Limits & Continuity — Quiz 1

Questions in this quiz (10)

1. $$\lim_{x\to3}\frac{2x^3-5x^2-x}{x-3}=$$

   • $$0$$
   • $$2$$
   • $$\infty$$
   • Do not exist

2. $$\lim_{x\to16}\frac{\sqrt{x}-4}{16-x}=$$

   • $$-\frac{1}{8}$$
   • $$\frac{1}{16}$$
   • $$-4$$
   • $$4$$

3. $$\lim_{x\to2}\frac{x^2-5x+6}{x-2}$$

   • $$-2$$
   • $$-1$$
   • $$2$$
   • $$4$$

4. $$\lim_{x\to-3}\frac{x^3+27}{x+3}=$$

   • $$3$$
   • $$9$$
   • $$27$$

5. If$$f(x)= \frac{x^2-4}{2-x}$$ $$x\ne2$$$$f(x)=1$$, $$x=2$$$$\lim_{x\to2}f(x)=$$?

   • $$-4$$
   • $$-2$$
   • $$2$$
   • $$4$$

6. $$\lim_{x\to0}\frac{|2x|}{x}=$$?

   • $$-1$$
   • $$-2$$
   • $$1$$
   • Does not exist

7. $$\lim_{x\to0}x\cos\left(\frac{1}{x}\right)=$$

   • $$0$$
   • $$1$$
   • $$-1$$
   • $$\infty$$

8. Find the value of $$k$$ that makes $$p$$ continuous if$$p(x)= |x-3|+k$$, $$x\le2$$$$p(x)= x^2-5x+6$$, $$x$$>$$2$$

   • $$-1$$
   • $$1$$
   • $$-\infty$$
   • $$\infty$$

9. On what interval must the function $$g(x)=x^2+5x-2$$ intersect the line $$y=4$$?

   • $$[-6,-4]$$
   • $$[-2,0]$$
   • $$[0,2]$$
   • $$[3,5]$$

10. Given a function $$h(x)$$ continuous on $$[2,6]$$ with $$h(2)=3$$ and $$h(6)=11$$, which of the following must be true? I. There exists a real number $$c$$ such that $$h(c)=7$$ II. $$h(4)=7$$ III. $$h$$ has a maximum and minimum on $$[2,6]$$

    • I only
    • III only
    • I and III
    • I, II, and III