Calc Jeopardy

Limits and Continuity

100

Evaluate: lim⁡x→2

(3x+1)

7

200

Evaluate: lim⁡x→0 

sin⁡x/x

1

300

Does lim⁡x→3    (x2−9/x−3) 

exist? If so, what is it?

Yes, 6

400

evaluate:lim  x→0    1-cos(2x)/x²

2

500

Is f(x)=x² -4/x-2 

continuous at x=2

Not continuous

Applications of Derivatives

100

What does the first derivative of a function tell you about its graph?

First derivative tells you increasing/decreasing and slope of the graph

200

Find the critical points of f(x)=x³-3x²

x=0,2

300

Determine intervals where f(x)=x/x²+1 is increasing or decreasing

increasing: (-∞,-1)U(1,∞)

decreasing: (-1,1)

400

A particle moves along a line: s(t)=t³-6t²+9t.  When is it at rest?

t=1,3

500

A rectangular field is to be fenced along three sides with 600 meters of fencing. One side is along a straight river and does not require fencing. What dimensions maximize the area of the field? What is the maximum area?

45,000 m²

Integrals

100

Evaluate: ∫x dx

1/2 x² + C

200

∫3x² dx

x³ + C

300

∫₀² (x² +1) dx

14/3

400

∫ x ⋅ cos(x²) dx

1/2 sin(x²)+C

500

∫ 1 / x²+1 dx

arctan(x) + c

The Fundamental Theorem of Calculus

100

F(x)=∫₀^x (2t+3) dt

Find F'(x)

F'(x)=2x+3

200

F(x)= ∫₁^x  sqrt(t²+1) dt

find F'(x)

F′(x)= sqrt (x²+1)

300

d/dx [∫₂^{x^2}  ln(t) dt] 

ln(x³)⋅3x²

400

∫₁⁴ (2x+1) dx

18

500

Pick Again

Pick Again