Post-Video Questions Preview

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Here are some questions you’ll be asked after you finish watching the videos. Please read through these before watching the videos.

If $f$ is a differentiable function and $a$ is in the domain of $f$ , then $f'(a)$ is given by which of the following expressions?

1. $\lim _{h \to 0} \dfrac {f(a+h)-f(a)}{h}$

2. $\lim _{x \to a} \dfrac {f(x)-f(a)}{x-a}$

3. $\lim _{h \to 0} \dfrac {f(x+h)-f(x)}{x-h}$

The expression $\lim _{h \to 0} \dfrac {e^{x+h}\sin (x+h)-e^x\sin (x)}{h}$ is the derivative of what function?

Which of the following statements represent the meaning of $f'(4.2) = 1.7$ ?

1. The slope of the line tangent to the graph of $y = f(x)$ at $x = 4.2$ is $1.7$ .

2. As $x$ increases by $1$ from $x = 4.2$ , $f(x)$ increases by $1.7$ .

3. The limiting value of the average rate of change of $f$ over the interval $[4.2, 4.2+\Delta x]$ as $\Delta x$ approaches zero is $1.7$ .