Show:
Limits
Derivatives
Implicit Differentiation
Area
Volume
100
What is the limit as x approaches 2 of (x^2-4)/(x-2)?
4
100
What is the derivative of f(x)=3x^2+9x+2+15x^4?
f'(x)=6x+9+60x^3
100
Find dy/dx of 2=xy+x^2.
dy/dx=-(y-2)/x
100
Find the area between the graph of y=3x+5 and the x-axis from x=1 to x=4 using left Riemann Sums of three equal intervals.
33
100
Find the volume of the solid created when R is rotated about the x-axis, where R is the region bounded by the graph of y=-x+3, x=0, and x=3.
9pi units cubed
200
What is the limit as x approaches infinity of (x^3+5x^2+2)/(3x^2+5+x^4)?
0
200
What is the equation of the line tangent to the graph of g(x)=2-x^3 at (2,-6)?
y=-12x+18
200
Find dy/dx for x^3+y^3=4.
dy/dx=-x^2/y^2
200
Using trapezoidal sums on four equal intervals, find the area between the graph of y=-x^2+4 and the x axis between x=-2 and x=2.
10
200
Find the volume of the solid formed by rotating R about the x-axis, where R is the region bounded by the graphs of y=x^3 and y=4x.
512pi/21 units cubed
300
What is the limit as x approaches 0 of 1/x^2?
Does not exist.
300
Find the first derivative of f(x)=[tan(x)]^2.
f'(x)=2tan(x)sec^2(x)
300
Find dy/dx for x=(x^2+y^2)^(1/2).
dy/dx=((x^2+y^2)^(1/2)-x)/y
300
Find the area bounded by the graph of y=-x^4+4 and the x-axis algebraically.
9.051
300
Find the volume of the solid generated by revolving the region bounded by the graphs of y=x^2 and y=4 about the line y=5.
832pi/15 units cubed
400
What is the limit as h approaches -2 of (h^3+8)/(h+2)?
12
400
What is the first derivative of f(x)=((3x^2-5)/(2x^2+7))^2?
f'(x)=124x(3x^2-5)/(2x^2+7)^3
400
Find y' of cos^2(x)+cos^2(y)=cos(2x+2y).
y'=(cos(x)sin(x)-sin(2x+2y))/(sin(2x+2y)-cos(y)sin(y))
400
What is the total distance traveled by a car with velocity v(t)=-(1/2)x+1 from t=0 to t=7?
7.25 units
400
Find the volume of the solid generated by revolving the region bounded by the graphs of y=x^2 and y^2=8x about the y-axis.
24pi/5 units cubed
500
What is the limit as x approaches -3/2 of (2x+3)/(4x^2+12x+9)?
Does not exist.
500
What is the third derivative of y=(2-9x)^1/3?
y'''=-270(2-9x)^(-8/3)
500
Find an equation of the line tangent to the graph of (x^2+y^2)^3 = 8x^2y^2 at the point (-1, 1) .
y=x+2
500
What is the area bounded by the graph of f(x)=(3x^3+x)^(1/2)-x^2 and the x-axis? Evaluate algebraically.
2.514
500
Find the volume of the solid made when R is rotated about the line x=3, where R is the region bounded by the graphs of y=x^2+1, x=0, x=2, and y=0.
16pi units cubed