Derivatives
Find d/dx of x^2
2x
Find the integral x^2. *Hint* Use the reverse power rule.
(x^3)/3 + C
Find the limit as x approaches infinity of ((4/X) - 7)
-7
Find the volume of the solid formed by rotating the region bounded by
y=x^2, x=0, and x=2, about the x-axis
32pi/5
Find the extreme values of the function and where they occur.
y=x^2 + 2x - 3
The minimum is -4 at x=-1
Find the average rate of change of the function over the given interval.
y = -3x^2 - x, [5,6]
-34
Find the integral of 2x/(x^2 + 3)
ln(x^2 + 3) + C
Find the limit as x approaches infinity of
(X^2 - 8X + 2)/(X^3 - 9X^2 + 15)
0
Find the volume of the solid formed by rotating the region between
y=sqrt(x) and y=1, x=0 and x=4, about the x-axis
4pi
Find the value or values of c that satisfy the equation (f(b)-f(a))/(b-a) = f'(c) in the conclusion of the mean value theorem for the function and interval.
f(x)=x^2 + 4x + 1, [2,3].
5/2
Find dy/dt of y = 2t(4t+5)^3
2(4t+5)^2 (16t+5)
Evaluate the integral from 0 to pi/16 of
24tan(4x)
3ln(2)
Use the limit as x approaches 0 of sin(x)/x = 1 to find the limit as x approaches 0 of tan(4x).
4
Find the volume of the solid generated by rotating the region bounded by
y=x, y=0, and x=1 about the y-axis.
2pi/3
Use implicit differentiation to find dy/dx
2xy - y^2 = 1
y/(y-x)
Find the derivative of y = (5/x) + 3sec(x)
y' = -(5/x^2) + 3sec(x)tan(x)
Evaluate the integral from 0 to pi/2 of
cos(x)/(3 + 4sin(x))^3
5/441
Find the limit as x approaches 0 of (sqrt(1+x) - 1)/x
1/2
Find the volume of the solid formed by rotating the region bounded by
y=x^2, y=0, and x=1 about the line y=-1
13pi/15
At the given point, find the slope of the curve.
y^5 + x^3 = y^2 + 9x, (0,1).
3
Find y'' of y = sqrt(7x+8)
-(49/(4(7x+8)^(3/2))
Find the derivative of the integral from 0 to x of sin(t).
5x^4 sin(x^5)
Find the limit as x approaches infinity of (4x - sqrt(16x^2 - 4x +3)).
1/2
Find the surface area of the solid formed by rotating the curve
y=sqrt(x), x=1, x=4, around the x-axis
about 30.52
Find the slope of the curve at the given point P and an equation of the tangent line at P.
y = x^2 + 5x, P(4,36).
The slope of the curve is 13 at P. The line y=13x-16 is tangent at P.