AP Calculus ABBC - Review #2

If

 $f'\left(x\right)=3e^{3x}\cos\left(e^{3x}\right)\$  , then  $f\left(x\right)=$  ?

•  $\cos\left(e^{3x}\right)$  

•  $e^{3\sin\left(x\right)}$  

•  $\sin\left(e^{3x}\right)$  

•  $\sin\left(3e^{3x}\right)$  

Tags

CCSS.HSF.TF.C.9

If $f\left(x\right)\ =\frac{\left(x-1\right)}{x+1}$ , then  $\frac{\left(f\left(b\right)-f\left(a\right)\right)}{b-a}$  is: 

• Positive on (-1, 1)

• Negative on (-1, 1)
  

• Undefined on (-1, 1)

• 0 on (-1, 1)

The function $g\left(x\right)=-\cos\left(x\right)$  is:

• Odd

• Even

• Neither Even or Odd

• A polynomial

Tags

CCSS.HSF.BF.B.3

Suppose that

 $\lim_{\left(x\rightarrow-2^-\right)}f\left(x\right)=k$  ,  $\lim_{\left(x\rightarrow-2^+\right)}f\left(x\right)=k$ , and  $f\left(-2\right)=k$ , then (Check all that apply)

• -2 is in the domain of  $f\left(x\right)$  

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

•  $f\left(x\right)$  has a removal at x = -2

•  $f\left(x\right)$  is continuous at x = - 2

•  $f\left(x\right)$  must be differentiable at x = -2

Suppose that $h\left(x\right)$  is continuous on the interval (2, 9) and that f(2) > 0 and f(9) < 0, then by the Intermediate Value Theorem

•  $f\left(x\right)\$  is decreasing on the interval (2, 9)

•  $f\left(x\right)\$  must have at least one x-intercept in the interval (2, 9)

•  $f\left(x\right)$  has a positive Average Rate of Change on the interval (2, 9)

•  $f\left(x\right)$  has at least one critical value in the interval (2, 9)

•  $\lim_{\left(x\rightarrow2\right)}f\left(x\right)=9$  

Suppose that $f'\left(9\right)=0\ and\ f''\left(9\right)>0$  then  $f\left(x\right)$  is _______________(two words) at x = 9.

The function sec x has ___ critical numbers in $\left(-2\pi,\ 2\pi\right)$  

• 0

• 1

• 3

• 5

• 7

 $\lim_{x\rightarrow3}\ \frac{\left(\left(x\right)^5-\left(3\right)^5\right)}{x-3}=$  ____

 $\lim_{x\rightarrow\pi}\ \ \frac{\left(\cos\ x+\sin\left(2x\right)+1\right)}{x^2-\pi^2}\ =$  ___

•  $\frac{1}{2\pi}$  

•  $\frac{1}{\pi}$  

• 1

• nonexistent

Tags

CCSS.HSF.IF.A.2

If $f\left(x\right)=\left(x-1\right)\left(x^2+2\right)^3\ ,\ \ then\ f'\left(x\right)\ is$  

•  $6x\left(x^2+2\right)^2$  

•  $6x\left(x-1\right)\left(x^2+2\right)^2$  

•  $\left(x^2+2\right)^2\left(x^2+3x-1\right)$  

•  $-3\left(x-1\right)\left(x^2+2\right)^2$  

•  $\left(x^2+2\right)^2\left(7x^2-6x+2\right)$