Differentiation
What is the derivative of f(x)=x3+4x-7
F(x)=(3/4)x4+(2/3)x3-5x+c
The region bound by the x-axis, y-axis, F(0) = 2, and F(4) = 8. What is the area?
Area = 20
Determine the limit by substitution:
limit as x approaches -1/2. f(x) = 3x2(2x-1)
-3/2
What are the conditions of the MVT?
-Differentiable on (a,b)
What is f'(1) if f(x)=(2x2)/(x2+5x)
f'(1)=5/18
F(x)=ln(x+1)+2x2+5
Region bounded by x-axis, y-axis, f(1) = 3, f(3) = 5, f(5) = 7, and f(7) = 10. Estimate the area from [1,7] using the trapezoidal rule.
Area = 37
Determine limit by substitution:
limit as x approaches -2: f(x) = (x-6)2/3
4
What classifies a point as extrema?
What is f'(x) if f(x)=arcTan(x)
f'(x)=1/(1+x2)
If f(x)=3x2(x3+23)4 find F(x).
F(x)=(1/5)(x3+23)5+C
Find the area bounded by the y-axis, f(x)=2x and g(x)=-4x2+5
Area=2.718
An object is dropped from the top of a 100 meter tower. It's height above ground after t seconds is 100-4.9t2 meters. How fast is the object falling 2 seconds after it is dropped?
19.6 meters/second
What classifies a jump discontinuity?
The limit as x --> # of f(x) is not equal to f(#)
Find f"(x) of f(x)=Cos(2x3+3)
f"(x)=-12x(Sin(2x3+3))-36x4(Cos(2x3+3))
What is the antiderivative of (1/(u ln(a)) du?
Logau
Find the volume of the solid whose region is a semicircle enclosed by y=(25-x2)1/2 and the x-axis from [-5,5]. The cross sections are squares, perpendicular to the x-axis.
(500/3)
Find the point(s) of discontinuity and the type.
f(x) = e1/x
0, infinite discontinuity
What are the 4 types of discontinuities?
Infinite, removable, jump, oscilating
Find dy/dx of x2+xy+y3=0
dy/dx=-(2x+y)/(x+3y2)
Find F(x) if f(x)=x(x+4)9 (Hint:This one is a little fancy)
F(x)=(1/11)(x+4)11-(2/5)(x+4)10+C
Find the volume of the solid when the region bounded by y=(x-1)1/2 and x-2y=1 is rotated about x=-1
Volume=9.6(pi)
Find the limit as x->2 of (x2-4)/(ln(x/2))
8
What is the second fundamental theorem of calculus?
d/dx (F(x)-F(#)) = f(x)dx