Unit 7 Review - Limits and Derivatives

Which of the following terms is NOT like the other one?

• Instantaneous velocity

• Slope of a tangent line

• Derivative

• Discontinuity

Evaluate  $\lim_{x\rightarrow\infty}\left(\frac{-5x^3-4x^2+x}{2x^4+x}\right)$  

•  $\frac{5}{2}$  

•  $1$  

•  $0$  

•  $-\frac{5}{2}$  

Shown is the graph of f(x) on the interval [-2,5].

Which of the statements is correct? SELECT ALL THAT APPLY.

• $\lim_{x\rightarrow1}\ f\left(x\right)=0$

• $\lim_{x\rightarrow4}\ f\left(x\right)=0$

• $\lim_{x\rightarrow0}\ \text{does not exist}$

The graph of the function f is shown. Which of the following statements is false?

• $\lim_{x\rightarrow2^-}\ f\left(x\right)=2$

• $\lim_{x\rightarrow4}\ f\left(x\right)=3$

• $\lim_{x\rightarrow2}f\left(x\right)\ \text{does not exist}$

• $\lim_{x\rightarrow2^+}f\left(x\right)\ \text{does not exist}$

Tags

CCSS.HSF.IF.A.2

Determine the value of  $\lim_{x\rightarrow\infty}\left(\frac{5x^3-4x^2+3x-8}{7x^3-x+1}\right)$  

•  $0$  

•  $\infty$  

•  $-\infty$  

•  $\frac{5}{7}$  

Find the derivative of  $\frac{1}{x^2}$  

•  $\frac{1}{2x}$  
  

•  $-\frac{2}{x^3}$  
  

•  $2x^{-1}$  
  

•  $-2x^{-1}$  
  

The graph of the function f is shown. The graph of f has horizontal tangent lines at  $x=-1$  and  $x=1$  and zeros at  $\left(-\sqrt{3},0\right),\ \left(0,0\right),\$  and  $\left(\sqrt{3},0\right)$  . 

For what interval(s) will f satisfy the conditions  $f'\left(x\right)<0\ \text{and}\ f\left(x\right)>0$  ?

•  $\left(-1,0\right)$  

•  $\left(-\sqrt{3},0\right)\cup\left(\sqrt{3},\infty\right)$  

•  $\left(-1,1\right)$  

•  $\left(-\sqrt{3},-1\right)\cup\left(\sqrt{3},\infty\right)$  

Tags

CCSS.HSA.APR.B.3

Jazmin's cat likes to jump off of high furniture at laser pointers. The cat's height above the laser point in feet can be modeled by the function  $h\left(t\right)=-16t^2+6$  , where t is measured in second.

Determine the cat's downward velocity at t = 0.5 seconds

• 8 ft/sec

• 10 ft/sec

• 16 ft/sec

• 2 ft/sec

Find the value of the first derivative of  $f\left(x\right)=4x^2-2x-1$  at the point where $x=2$  

• 11
  

• 15

• 16

• 14

Find the equation of the line tangent to the function at the given point:

 $y=x^2-4x+5\ \ \text{at}\ \left(2,1\right)$  

•  $y=-8x+1$  
  

•  $y=-10x-4$  
  

•  $y=1$  
  

•  $y=-12x-11$