AP Calc Ab Review Jeopardy

Limits

100

What is the limit of f(x)=3x+2 as x approaches 1?

5

200

How do you evaluate lim _x→0⁡ sin⁡x/x?

1

300

If g(x)<f(x)<h(x) on (a,b) and lim_x->0g(x)=1 and lim_x->0h(x)=1 then the lim_x->0f(x) must be?

What is 1?

400

Find lim⁡_x→2(x²−4)/(x−2)

4

500

Explain the concept of one-sided limits and calculate lim⁡_x→3 −(x²−9)/(x−3)

6

Derivatives

100

The derivative of 3.

What is 0?

200

 What is the derivative of f(x)=x³?

3x²

300

 Find the derivative of f(x)=sin⁡x

cosx

400

Use the product rule to differentiate f(x)=x²⋅ln⁡x

f(x)=2xln(x)+x

500

 What is the second derivative of f(x)=e^x+3?

e^x

Implicit Defferentiation

100

The derivative of y?

What is dy/dx?

200

Differentiate the equation x²+y²=25 implicitly.

-x/y

300

If x³+y³=6xy, find dy/dx.

dy/dx= 3x²-6y/6x-3y²

400

Differentiate the equation sin⁡(xy)=x+y implicitly.

cos(xy)(y+x(dy/dx))=1+(dy/dx)

500

Solve for dy/dx in the equation x²y+3y=7.

dy/dx = -(2xy/x²+3)

Contextual Applications of Derivatives

100

What does it mean for a function to be increasing or decreasing based on its derivative?

A function is increasing if it's derivative is positive and decreasing is its derivative is negative

200

How can you use derivatives to find the maximum or minimum of a function?

Locate points where f'(x) = 0 or is undefined then use the second derivative test to confirm

300

Describe the relationship between the first derivative and the slope of a tangent line.

the first derivative of the funtion at a point gives the slope of the tangent line to the curve at that point

400

How can you interpret the derivative of a position function?

f' of a position function represents velocity which indicates speed and direction of motion

500

Explain how derivatives are used in related rates problems with an example.

in a related rates problem, derivatives represent the rate of change of quantities with respect to time. EX: A=(pi)r² with respect to time relate dA/dt to dr/dt

Analitical Applications of Derivatives

100

What is the purpose of the Mean Value Theorem?

there is a point where the instantaneous slope of the tangent = the avarage rate of change over the interval

200

State the Fundamental Theorem of Calculus.

the value of any function is the rate of change (the derivative) of its integral from a fixed starting point up to any chosen end point.

300

How do you determine concavity using the second derivative test?

The second derivative test determines concavity. If f"(x) is less than 0 the function is concave up and if f"(x) is less than 0 than the function is negative

400

lim_x->0(1-cos(2x)/(5x)

What is 0?

500

The vertex of x²+2x+1

What is (-1,0)?