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Level 594

Calculus BC


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cos(x)
Derivative: sin(x)
-sin(x)
Derivative: cos(x)
sec²(x)
Derivative: tan(x)
-csc(x)cot(x)
Derivative of csc(x)
sec(x)tan(x)
Derivative: sec(x)
-csc²(x)
d/dx cot(x)
1/√(1-x²)
Derivative: sin⁻¹(x)
-1/√(1-x²)
Derivative: cos⁻¹(x)
1/(1+x²)
Derivative: tan⁻¹(x)
-1/(1+x²)
Derivative: cot⁻¹(x)
1/(x√(x²-1))
Derivative: sec⁻¹(x)
-1/(x√(x²-1))
Derivative: csc⁻¹(x)
1/ƒ'(y)
Derivative: ƒ⁻¹(x)
y'
Derivative: y
Horizontal Tangent Line
The tangent line to a point where ƒ'(x)=0
Vertical Tangent Line
the tangent line to a point where ƒ'(x) fails to exist
(dV/dt) = 2πr(dr/dt)h + πr²(dh/dt)
The derivative of V = πr²h with respect to time
csc(x)=
1/sin(x)
sec(x)=
1/cos(x)
tan(x)=
sin(x)/cos(x)
cot(x)=
cos(x)/sin(x)
V=(4/3)πr³
Volume of a Sphere
V=πr²h
Volume of a Circular Cylinder
V=(1/3)πr²h
Volume of a Circular Cone
they are similar triangles with equal proportions
The relationship between an amount in a cone and the dimensions of the cone is
SA=6x²
The Surface Area of a Cube
SA=4πr²
Surface Area of a Sphere
SA=2πr² + 2πrh
The Surface Area of a Cylinder w/Top and Bottom
Max and Min Values live where
The first derivative equals zero or FTE
C=2πr
Circle (circumference)
A=πr²
Area formula with radius
The graph is above the x-axis
If given the graph of a function, the function is positive when
Points of Inflection
The max and min on a graph of the derivative are the what of the original function
The slope of ƒ'(x)
A geometric meaning of ƒ''(x)
Geometric series convergence
If |r|<1, the series converges
∑arⁿ⁻¹
Geometric series layout
S=a/(1-r)
Sum of geometric series
Sequence convergence/divergence
Lim(n→∞) aⁿ = L
lim(n→∞) aⁿ⁺¹/aⁿ
What is the ratio test?
Ratio test conditions
If p<1, the series converges
∑(-1)ⁿ⁺¹bⁿ
Alternating series layout
bⁿ>0
Conditions for series convergence