Derivatives
Limits
Antiderivative/Integrals
Miscellaneous
100
The derivative of y=15x4 + 8x2 - 10x +6
y'=60x3 + 16x - 10
100
lim (2x+5)
x-> 2
2(2)+5
4+5
=9
100
∫ 1/x2 dx =
−x−1 +C
100
This curve is closed to the x-axis when finding areas with more than one curve.
What is a minor curve?
200
The derivative of y=xsinx
y'=sinx+xcosx
200
lim (x-4)/(x2-8x+16)
x -> 4
DNE
200
∫(x/x2-4)dx=
1/2 ln|x2−4|+C
200
This theorem states that if f(x) is defined and continuous on the interval [a,b] and differentiable on (a,b), then there is at least one number c in the interval (a,b) such that a < c < b.
What is the Mean Value Theorem?
300
The derivative of y=14x4 + cscx
y'= 56x3 - cscxcotx
300
When does a limit not exist?
(List all)
1) When there is jump discontinuity (left and right are not equal)
2) When there is oscillation
3) When there is a vertical asymptote
300
∫(sin(2x)+cos(2x))dx =
−1/2cos(2x)+1/2sin(2x)+C
300
A functions fails to be differentiatioble if it has a...
What is a discontinuity/vertical tangent
400
The derivative of y=ex / x+1
y'= xex / (x+1)2
400
lim (sin x) / x
x -> 0
= lim (cos x/1) = lim (cos x)
x -> 0
= cos (0) = 1
400
If ∫03 f(x) dx=6, and ∫35 f(x)dx=4, then ∫05 (3+2f(x))dx= ?
35
400
This method is when all cross sections to find a volume will be in circle form, the formula for the cross section is A(x)= A= pi r^2.
What is the Disk Method?
500
The derivative of y=(1+ sin9(2x+3))2
y'= 2(1+sin9(2x+3))⋅9sin8(2x+3)⋅cos(2x+3)⋅2
500
lim (1/2x+sinx)
x -> 3
= 1/ 2(3) + sin (3)
= 1/6+sin(3)
500
∫(ex^1/2/x1/2) dx
2ex^1/2 + C
500
Find any points where the graph fails to be differentiatioble and explain why 3√(5x+7)
What is y is not differentiable at x=-7/5 due to vertical tangent