Week7a

Question.

Let $f(x)=\sqrt{x}$. The derivative $f'(x)$ is expressed by the following limit:

a) $\lim_{h\rightarrow 0} \dfrac{f(\sqrt{x+h})-f(\sqrt{x})}{h}$

b) $\lim_{h\rightarrow 0} \dfrac{(\sqrt{x}+h)-\sqrt{x}}{h}$

c) $\lim_{h\rightarrow 0} \dfrac{\sqrt{x+h}-\sqrt{x}}{h}$

d) $\lim_{h\rightarrow 0} \dfrac{\sqrt{x+h}-x}{h}$

Question.

Let $f(x)=\sqrt{x}$. The derivative $f'(4)$ is expressed by the following limit:

a) $\lim_{h\rightarrow 0} \dfrac{\sqrt{4+h}-2}{h}$

b) $\lim_{h\rightarrow 0} \dfrac{\sqrt{x+4}-\sqrt{x}}{h}$

c) $\lim_{h\rightarrow 0} \dfrac{\sqrt{4+x}-2}{4}$

d) $\lim_{h\rightarrow 0} \dfrac{(2+\sqrt{x})-2}{h}$

Question.

The limit $\lim_{h\rightarrow 0} \dfrac{(x+3+h)^2-(x+3)^2}{h}$ represents the derivative of which function?

a) $x^2$

b) $x^2+3$

c) $(x+3)^2$

d) $2(x+3)$

Question.

Suppose that $f(x)$ is a continuous function with $f(2)=15$ and $f'(2)=3$. Estimate $f(2.5)$.

a) 10.5

b) 15

c) 16.5

d) 18

Question.

Let $C(x)$ be the total cost of producing $x$ feet of Christmas lights. Which of the following statements is true?

a) $C'(20)<C'(30)$

b) $C'(20)=C'(30)$

c) $C'(20)>C'(30)$

d) Not enough information.

Question.

If $f'(a)$ exists, then $\lim_{x\rightarrow a} f(x)$

a) must exist

b) equals $f(a)$

c) equals $f'(a)$

d) may not exist.

Navigation menu