Differentiation — Quiz 4

Questions in this quiz (10)

1. Find$$\lim_{x\to\infty}\frac{\ln x}{x^2}$$

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

2. Find$$\lim_{x\to-3}\frac{x^3+27}{x^2-9}$$

   • $$-3$$
   • $$3$$
   • $$-\frac{9}{2}$$
   • Does not exist

3. Find$$\lim_{x\to\infty}x\sin\left(\frac{2}{x}\right)$$

   • $$0$$
   • $$1$$
   • $$2$$
   • Does not exist

4. Find$$\lim_{x\to0}(1+3x)^{\frac{1}{x}}$$

   • $$e$$
   • $$e^3$$
   • $$3$$
   • $$1$$

5. Find$$\lim_{x\to\infty}x^{\frac{2}{x}}$$

   • $$0$$
   • $$1$$
   • $$2$$
   • $$e^2$$

6. Find$$\lim_{h\to0}\frac{(3+h)^3-3^3}{h}$$

   • $$9$$
   • $$18$$
   • $$27$$
   • $$36$$

7. Find$$\lim_{h\to0}\frac{e^{3h}-1}{h}$$

   • $$1$$
   • $$3$$
   • $$e^3$$
   • $$0$$

8. Find$$\lim_{h\to0}\frac{1}{h}\left(\frac{1}{2+h}-\frac{1}{2}\right)$$

   • $$-\frac{1}{4}$$
   • $$-\frac{1}{2}$$
   • $$\frac{1}{2}$$
   • $$\frac{1}{9}$$

9. If $$f(x)=9\sqrt{x}$$, then $$f''(1)$$ is equal to:

   • $$-\frac{9}{4}$$
   • $$-\frac{3}{4}$$
   • $$-9$$
   • $$-\frac{9}{2}$$

10. If a point moves on the curve $$x^2+y^2=16$$ then at $$(4,0)$$, $$\frac{d^2y}{dx^2}$$ is:

    • $$0$$
    • $$-\frac{1}{4}$$
    • $$\frac{1}{4}$$
    • Undefined value