Unit Physics Test 11/13

We have learned that if we take the limit of the slope while the difference between points approaches zero, we get a quantity called the

The derivative of position is

• Acceleration

• Velocity

• Position

• Jerk

What are the two ways to write a derivative?

• $f'\left(x\right)$

• $\frac{\text{d}f}{\text{d}x}$

• $\int x\ dx$

• $\lim_{x\rightarrow y}f\left(x\right)$

The derivative of velocity is

• Acceleration

• Velocity

• Position

• Electromagnetic Flux

What is the derivative of

 $f\left(x\right)\ =\ x^2$  

• 2x

•  $\frac{x^3}{3}+c$  

• cos(x)

• 0

Taking the derivative of a constant C results in the value of

• 0

• C

• Cx

• sin(Cx)

If you have a function within a function, which rule would you have to use to take their derivatives?

• Power Rule

• Chain Rule

• Product Rule

• Exponential Rule

The derivative of

 $f\left(x\right)\ =\ \left(x^2-4\right)\left(3x+6\right)$  is

•  $\left(x^2-4\right)\left(3\right)\ +\ \left(2x\right)\left(3x+6\right)$  

•  $0$  

•  $\left(x^2-4\right)\left(3\right)-\left(2x\right)\left(3x+6\right)$  

• 2x +3x

For the next few problems you will use the limit definition of the derivative. What is this limit?

• $\lim_{0\rightarrow h}\ \frac{f\left(x+h\right)-f\left(x\right)}{h}$

• $\lim_{h\rightarrow0}\ \frac{f\left(x+h\right)-f\left(x\right)}{h}$

• $\lim_{h\rightarrow\pi}\ \frac{\sin\left(x\right)}{h}$

• $\lim_{h\rightarrow0}\ \frac{f\left(x-h\right)+f\left(x\right)}{h}$

According to the limit definition of the derivative, why does the derivative of a constant equal zero?

• Because the function does not change, therefore the numerator will be zero before you take the limit, resulting in the value of zero.

• Because the function changes constantly, therefore the denominator will approach zero and result in an asymptote

• Because the limit definition of the derivative says so

• Because the denominator of the functions will vanish.