Calc Quiz 2.1

f'(x)=            

 (there may be more than one answer)

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

• $\lim_{x\rightarrow c}\left(\frac{f\left(x\right)-f\left(c\right)}{x-c}\right)$

• $\frac{\text{d}y}{\text{d}x}$

• an equation for the slope of the tangent line

 $\lim_{h\rightarrow0}\left(\frac{5\left(x+h\right)^2-5x^2}{h}\right)$  

•  $5x^2$  

•  $10x$  

• 10

• DNE

Tags

CCSS.HSA.SSE.A.2

CCSS.HSA.SSE.B.3

CCSS.HSA.APR.A.1

Use the limit definition to find the value of the derivative at the indicated x-value.

• -4

• 3

• 0

• 24

 $\lim_{x\rightarrow-3}\ \ \frac{x+3}{x^2-9}\ =\ ....$  

• 0

•  $-6$ 

• 6

•  $-\frac{1}{6}$  

•  $\frac{1}{6}$  

Tags

CCSS.HSA.SSE.A.2

CCSS.HSA.SSE.B.3

CCSS.HSA.APR.D.6

CCSS.HSA.APR.D.7

 $\lim_{x\rightarrow-5}\ \ \ \frac{x+5}{2}\ =\ ....$  

• 0

• 5

•  $\infty$  

•  $\frac{5}{2}$  

•  $\frac{2}{5}$  

Use the limit definition to find the slope of the graph of f(x) at (3,2). $f\left(x\right)=11-x^2$  

Use the limit definition to find the derivative of the function.

 $f\left(x\right)=2x^2+7x$  

Use the limit definition to find the derivative of the function.

 $f\left(t\right)=\sqrt{t+2}$  
when typing your answer, type sqrt for the square root and put whatever is under the root in parentheses. Use * for multiplication. If there is more than one part to your numerator or denominator, be sure to use parentheses.

Find an equation of the tangent line to the graph of   $f\left(x\right)=\frac{1}{x-3}$   at (2,-1).