AB Calculus Limits Test

Evaluate the limit  $\lim_{x\rightarrow0}\left(\frac{5x^4+8x^2}{3x^4-16x^2}\right)=$  

Evaluate the limit:  $\lim_{x\rightarrow1}\left(\frac{7x-18}{\left(x-2\right)^2}\right)=$  

Evaluate the limit:  $\lim_{x\rightarrow\infty}\left(\frac{5x^3+2x-1}{2x^3-9}\right)=$  

Evaluate the limit:  $\lim_{x\rightarrow4^-}\left(\frac{2}{x-4}\right)=$  

If  $f\left(x\right)=x^2$  determine the value of  $\lim_{x\rightarrow0}\left(\frac{f\left(3+x\right)-f\left(3\right)}{x}\right)=$  

Given $\lim_{x\rightarrow\infty}f\left(x\right)=-2$ which statement must be true?

•  $f\left(0\right)=-2$  

• There is a horizontal asymptote at y = -2

•  $f\left(x\right)\ne-2\$  for all  $x\ge0$  

•  $\lim_{x\rightarrow-\infty}f\left(x\right)=-2$  

• None of the above

Tags

CCSS.HSF-IF.C.7E

Given the function  $f\left(x\right)=4x^2-x$  
Determine the average rate of change over the interval [-1,2]

Tags

CCSS.8.F.B.4

CCSS.HSF.IF.B.6

The graph represents f(x)

Find  $\lim_{x\rightarrow1}f\left(x\right)$  

• 2

• -4

• DNE

• -2

Tags

CCSS.HSF.IF.A.2

The graph represents f(x).
Find  $\lim_{x\rightarrow6}f\left(x\right)$  

• DNE

• 1

• 5

• -2

• -7
• 0
• 1
• DNE

Tags

CCSS.HSA.REI.D.10