Calculus Jeopardy

Limits and Continuity

100

A vertical asymptote is an example of this type of discontinuity...

What is infinite discontinuity?

200

A "hole" in a function is an example of this type of discontinuity...

What is removable discontinuity?

300

The limit as x approaches 0 for f(x) = sin(x)/x is

1

400

How many conditions must be satisfied for a function to be continuous at x = a?

3 conditions

500

This theorem can be used to prove the existence of roots on interval [a, b]

The Intermediate Value Theorem

Basic Derivatives

100

f(x) = |x|, then f'(0) =

DNE

200

If f(x) = x² + 1, and g(x) = 1 - x², then [f(x) + g(x)]' =

0

300

If y = x² / (x - 1), then dy/dx at x = 2 is

0

400

If f(x) = x² and g(x) = x³ - 2, then [f(x)g(x)]' at x = 2 is...

72

500

If f(x) = 1/x², then f'(0) = 

DNE

Derivatives of Inverse Functions

100

If y = sin^-1(x), the dy/dx = 

1 / √(1 - x²)

200

If y = e^2x, then dy/dx is

2e^2x

300

If y = log₂(x³), then dy/dx is

(3)[1 / xln(2)]

400

y = e^sin(2x), then y' = 

2e^sin(2x)cos(2x)

500

If y = 2^x, then what is the equation of the tangent line at x = 0?

y = xln(2) + 1

Applications of Differential Calculus

100

A circle is expanding, find an expression for how the circumference is changing.

dC/dt = 2𝜋(dr/dt)

200

An ice-cube is melting. If the side-length is decreasing by -2 cm/s, then at what rate is the surface area changing when s = 1?

dA/dt = -24 cm²/s

300

If y = (x² - x) / (e^x - 1), then what is the limit as x approaches 0?

-1

400

If f'(c) = 0 and f''(c) < 0, then what can we conclude?

There exists a local maximum at x = c; f(c) = local maximum.

500

When the average rate of change is equal to the instantaneous rate of change.

What is the Mean Value Theorem?

Integral Calculus

100

f(x) = x² - 8x + 1, then what is the antiderivative F(x)?

(1/3)x³ - 4x² + x + C

200

If f(x) = sec²(x), then what is the area under the curve on [0, 𝜋/3]?

√3

300

Given f(x) = 2/x, what is the area under the curve on [1, e]? 

2

400

If f(x) = x^-2/3 + x, then what is the area under the curve on [0, 1]?

3.5 or 7/2

500

If f(x) = cos(2x), then what is the area under the curve on [0, 𝜋/6]?

√3 / 4