Calculus Final Project Jeopardy

Unit 1-Limits

100

A POD forms when both the numerator and denominator share this aspect

Common factor

200

Evaluate 

   lim         x + 5 

 x -> 4      x - 4

DNE

300

Determine 

  lim          5x² + 16x + 3 

x -> ∞          9x² - 4

5 / 9

400

Find the value k for which the limit exists: 

     lim       -4x² + kx + 7k - 6 

   x -> 3         2x² - 5x - 3

k = 3

Unit 2-Derivatives

100

Along with corner, cusp, and a discontinuity, a function is non-differentiable at this feature

Vertical tangent

200

The derivative of y = (9x + 3)³

27(9x + 3)²

300

The equation of the tangent line to y = 5/(x - 4) at x=-6, in point-slope form

y + 1/2 = -1/20 (x + 6)

400

Find dy/dx of 

x² =  x - y 

        x + y

dy/dx = y/x - (x + y)² 

Unit 3-Trig, Log, Exponential derivatives, and Applications

100

When can we use L’Hopital’s Rule

When the limit is indeterminate

200

y' if y = cos(5x)

y' = -5 sin(5x)

300

Find the derivative of 

y =  (3x + 5)¹³ log(1) 

            (7 - 4x)⁹ 

0

400

Determine where the slope of y = e^2x + 3 is the same as the y-coordinate

x = ln(3) / 2

Unit 4-Integration

100

The approximation of area under a curve using a finite number of rectangles is called this kind of sum.

Riemann Sum

200

Find the antiderivative of f(x) = 4x

F(x) = 2x² + c

300

Find the antiderivative of          x cos(2x²) 

1/4 sin(2x²) + c

400

Evaluate the integral of (x³ + 2)^1/2 x² dx

2/9 (x³ + 2)^3/2 + c