Thanksgiving review AP Calculus

• -2 sin 2x
  

• - sin 2x

• sin 2x

• 2 sin 2x

• 2 sin x

• 1/3

• 3/4

• 3/2

• 9/4

• infinite

• $5\left(1\ +\ x\right)^4$

• $\frac{x^4}{\left(x\ +\ 1\right)^4}$

• $\frac{5x^4}{\left(x\ +\ 1\right)^4}$

• $\frac{5x^4}{\left(x\ +\ 1\right)^6}$

• $\frac{5x^4\left(2x\ +\ 1\right)}{\left(x\ +\ 1\right)^5}$

• $f\left(x\right)=x^2\ +\ 2x$ and $g\left(x\right)\ =\ x^2\ +\ \ln\ x$

• $f\left(x\right)\ =\ 3x^3$ and $g\left(x\right)\ =\ x^4$

• $f\left(x\right)=3^x$ and $g\left(x\right)\ =\ x^3$

• $f\left(x\right)\ =\ 3e^x\ +\ x^3$ and $g\left(x\right)\ =\ 2e^x\ +\ x^2$

• $f\left(x\right)\ =\ \ln\left(3x\right)$ and $g\left(x\right)=\ln\ \left(2x\right)$

• $\left[0,\ \infty\right)$ only

• $\left(-\infty,\ 0\right]$ only

• $\left[-\frac{1}{\sqrt{3}},\ \frac{1}{\sqrt{3}}\right]$ only

• $\left(-\infty,\ \infty\right)$

• There is no such interval

• x = 3 only

• x = 4 only

• x = 0 and x = 2

• x = 0 and x = 3

• x = 0 and x = 4

The table gives selected values for a twice-differentiable function f. Which of the following must be true?

• f has no critical points in the interval -1 < x < 5

• f'(x) = 8 for some value of x in the interval -1 < x < 5

• f'(x) > 0 for all values of x in the interval -1 < x < 5

• f''(x) < 0 for all values of x in the interval -1 < x < 5

• The graph of f has no points of inflection in the interval -1 < x < 5

• $\frac{8}{\pi}$

• 16

• 40

• $40\pi$

• $80\pi$

• $\sqrt{\frac{7}{3}}$

• $\sqrt{\frac{13}{3}}$

• $\sqrt{5}$

• $\sqrt{6}$

• $\sqrt{\frac{19}{3}}$

The graph of a function f is shown. Which of the following limits does not exist?

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