Calculus Jeopardy

Derivatives

100

Sinx

Cosx 

200

Cotx 

-Csc²X

300

e^x

e^x

400

ln

1/x

500

a^x

a^xlna 

linear approximation

100

List the steps 

1. Get the equation of the tangent line

2. Then get the estimate

200

Suppose it is known for a given diffeenciable function f(x) than its lineaization at the point X=4 it is given by L(x)= 3(x-4)-2 use to estimate f(5.2)

Y=3(x-4)-2

300

Suppose it is known for a given diffeenciable function f(x) than its lineaization at the point X=4 it is given by L(x)= 3(x-4)-2 use to estimate f(5.2)

Y=3([5.2]-4)-2

y=1.6

400

F(x)=4x^-1/3

What is the approximation for f(-.9) found by using the line tangent to the graph of f(x) at x=-1

Y=-4.13

500

Is the estimate found of f(-.9) an under estimate or an overestimate

Underestimate 

L’hospitals Rule

100

Line X—> 4

x²-16/x-4

lim x—> 4 = 8

200

Lim x—>1 

5x⁴-4x²-1/10x-x-9x³

3/-7

300

Lim x—>0

5sin(3x)/2(0)

15/4

400

Lim x—>1

lnx/3-2x-x²

1/-4

500

Lim x—>3

2x²-4/x

14/3

definite Integral

100

{1     (X²+2)dx 

{-1 

14/3

200

{4      X(3x²-2)dx

{0

176

300

{(3x-5)²dx

3x³-15x²+25x+c

400

{(3x-5)¹⁰dx

1/33(3x-5)¹¹+C

500

{3x²SquareRoot 2x-4dx

1/3(2x³-4)^3/2+C

Random

100

If f(x)=4/x+5x-1, then f’(2) is…

4

200

What is the equation of the line tangent to f(x)=4x³-5x+3 when x=-1

Y=7x+11

300

Simplified derivative of: f(x)=(-5x³+2)(x²+2)

f’(x)=-25x⁴-30x²+4x

400

Write the equation of the line to f(x)=2x²+4x-2 with a slope of -8

Y=-8x-20

500

Lim x—>0 x³-6x+8/x-2

-4