Kassandra's Calc AB Review Game

Limits

100

lim as x approaches 0 for the function f(x)=(6x+4)/(3x-1)

-4

200

lim as x approaches infinity of the function f(x)= (10x+3)/(5x-9)

2

300

lim as x approaches 3 of the function f(x)=(2(x^2)-x-15)/(x-3)

11

400

lim as x approaches 1 of the function f(x)=((x^3)-1)/(x-1)

3

500

the values for a and b that make the function f(x)= a-4x(x<1) and (x^2)+b (x>/=1) continuous are 

a=7

b=2

Derivatives

100

the derivative of the function f(x)= (x^8)+13(x^6)-6(x^3)+x+19 

8(x^7)+78(x^5)-18(x^2)+1

200

the derivative of the function f(x)=(2(x^3)+3)/(3x-4) is

12(x^3)-24(x^2)-9 / (3x-4)^2

300

find the tangent line of the function f(x)=sin(pi*x)+1 at x=1 

y-1=pi(x-1) 

400

the derivative of the function f(x)=ln(3(x^2)+9)^1/2

x/(x^2)+3

500

the dy/dx of the equation 2(x^2)+2(y^2)=8 is 

-x/y

Integrals

100

the left Riemann sum for the function f(x)=3x+2 between x=0 and x=5 and using 5 rectangles is 

40 

200

the trapezoidal sum of the area under the function f(x)= (x^2)+2x+1 between x=0 and x=4 in 4 equal parts is 

42

300

the area between the functions f(x)=(x^2)+3 and g(x)=0.5x+10 is 

25.025

400

the change in position of a particle, which is represented by the function v(t)= 5x+4, between t=2 and t=10 is 

272 units

500

the volume of a shape created by revolving the function f(x)=3(x^2)+8x-7 from x=0 to x=3 around the x axis is

120.4*pi units^3

f/f'/f''

100

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The function above has a positive derivative between the x values: 

[0,2]

200

when the graph of a particle in motion has a negative derivative and a negative second derivative at t=a, the particle is 

speeding up

300

the function f(x)=(x+2)^3/ (x-5) is concave up between the interval 

(-infinity, -2)U(5, infinity) 

400

the inflection points of the function f(x)=(x+3)^3 + x^2 are 

x= (-10/3), (299/27) 

500

the tangent line for the function f(x)=-3(x^3)+2(x^2)+8x+2 at x=2 is

above the curve

Random questions

100

A 13 foot ladder is slowing sliding down a wall at a rate of .5 ft/ second. Before the ladder starts sliding down the wall, the ladder's tip is 12 feet from the floor. At what rate is the base sliding horizontally when the height from the floor is 7 feet? 

6/5 ft/sec

200

The characteristics that define a function as differentiable are

continuous and has a definitive derivative at all points

300

when a particle who's motion is represented by a function has an f(a)' that is positive and f(a)'' is negative, the particle is

slowing down

400

the implicit derivative of the function 2(x^2)y+5y^2=7x is

dy/dx= (7-4xy)/(2(x^2)+5y)

500

the derivative of the function f(x)=tan(pi+x)3(x^2)

6xtan(pi+x)+3(x^2)sec^2(pi+x)