AP Calculator Worksheet

How many x-intercepts does the function $f\left(x\right)=30x^3-2^x$ have?

• 0

• 1

• 2

• 3

How many x-intercepts does the graph of $f\left(x\right)=\sin\left(\frac{1}{x}\right)$ in the interval [0.01,1]? 

• 3

• 5

• 7

• 9

• infinitely many

How many intersection points do these two functions have? $f\left(x\right)=.3x,\ g\left(x\right)=\sin x$  

• 0

• 1

• 2

• 3

• 4

How many intersection points do these two functions have? $f\left(x\right)=.3x,\ g\left(x\right)=x\sin x$  

• 3

• 5

• 7

• 9

• infinitely many

Solve $x^3+3\sin\left(x+1\right)=1.$  

• x = -0.817

• x = -0.587

• x = 0

• x = 0.327

• x = 0 or x = -1.722

Solve $3\sin\left(x-1\right)+4\cos\left(x^2+1\right)=x,$  on the interval [-4,-2].

• -2.694, -3,059, -3.740

• -2.002

• -3.082

• -2.303, -2.750, -3.298, -3.825

• No solutions

Find the slope of f at point x = a:
 $f\left(x\right)=\sin\left(\cos x\right),\ a=1$  

• -0.941

• -0.867

• -0.722

• -0.258

• 0.540

Find the slope of f at point x = a:
 $f\left(x\right)=3x^4-\sin x,\ a=0.21$  

• -0.941

• -0.867

• -0.203

• 1.089

• None of these

Find the area under the curve y = f(x) for  $-1\le x\le1$  
 $f\left(x\right)=5x^3-\cos\left(\ln x\right)$  

• 17.842

• 98.481

• 99.232

• 99.482

• DNE

Find the area under the curve y = f(x) for $-1\le x\le1$
 $f\left(x\right)=\frac{\sin x}{x}$ 

• 0

• 0.946

• 1.571

• 1.683
  

• 1.892