AP Calculus ABBC - Review #3

 $\lim_{x\rightarrow0}\ \frac{3x}{\cos\ x}$  = ___

 $\lim_{x\rightarrow5^{-\ }}\ \frac{\sqrt{25-x^2}}{x-5}$  =

• 0

•  $\infty$  

•  $-\infty$  

• Undefined

Find the horizontal asymptote of 

 $f\left(x\right)=\frac{\left(x^3+5\right)}{x}$  

•  $y=0$  

•  $x=0$  

•  $f\left(x\right)$  has no horizontal asymptote because  $\lim_{x\rightarrow\infty}\ f\left(x\right)=\infty$  

•  $y=1\ and\ x=-5$  

Tags

CCSS.HSF-IF.C.7D

At what values of x is

 $f\left(x\right)=\frac{\left(x+5\right)}{x^2-x-2}$  discontinuous? (Check all that apply)

• x = 0

• x = -1

• x = 2

• x = -5

•  $f\left(x\right)$  is never discontinuous

Tags

CCSS.HSF-IF.C.7D

In order for

 $g\left(x\right)\$  to be continuous at  $x=a$  : (Check all that apply)

•  $\lim_{x\rightarrow a}\ g\left(x\right)=g\left(a\right)$  

•  $\lim_{x\rightarrow a}\ g\left(x\right)\ must\ exist$  

•  $g\left(a\right)\ must\ exist$  

•  $\lim_{x\rightarrow\infty}\ g\left(x\right)=a$  

•  $\lim_{x\rightarrow a^{-\ }}g\left(x\right)\ and\ \lim_{x\rightarrow a^+}\ g\left(x\right)\ may\ or\ may\ not\ be\ equal$  

Use the table to estimate  $f'\left(2\right)$  

• 1.8

• 5.6

• 3.7

• 3.6

• 1.7

Tags

CCSS.HSF.IF.A.2

Let $f\left(x\right)=5x\ \csc\ x$ , find  $f'\left(x\right)$  

•  $-5\csc^2x$  

•  $5\csc x\cot x$  

•  $5\csc x\left(1-x\cot\ x\right)$  

•  $-\frac{5}{\sin^2x}$