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AP CALCULUS AB

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Section 1

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Trig Identities

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Calculus Math

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Mar 1, 2020

Cards (39)

Section 1

(39 cards)

Trig Identities

Front

Back

Differentiation: Logarithms

Front

d/dx of ln|x| = 1/x d/dx of log base a of |x| = 1/(ln(a)x) d/dx of ln|f(x)| = f`(x)/f(x)

Back

Differentiation: Implicit Functions

Front

Back

Differentiation: Product Rule

Front

Back

Disk Volume

Front

Back

Riemann Sum: Trapazoidal

Front

http://images.slideplayer.com/22/6418662/slides/slide_4.jpg

Back

Inflection Points

Front

To find inflection points 1. Find the second derivative 2. Set the second derivative equal to zero 3. Solve for x Optional 4. Plug in and solve for f(x)

Back

Indefinite Integral

Front

Back

Washer Volume along y axis

Front

Same as along the x axis simply replace x with y (replace every single x with a y)

Back

Linear Approximation

Front

F(x)~=~f(a) +f`(a)(x-a)

Back

Integration: Trig Functions

Front

http://calculus.nipissingu.ca/tutorials/integralgifs/int_indef_trigtable.gif

Back

Optimization with Constraint

Front

1. Visualize the problem; name the variables 2. Write down the objective function - the one to be optimized - as a function of two variables 3. Write down a Constraint Equation relating the variables 4. Use the constraint to rewrite the objective function in terms of one variable (Isolate one of the variables and then plug in for that variable) 5. Analyze the new function of one variable to find its optimal point(s) and the optimal value

Back

Riemann Sum

Front

Back

Intermediate Value Theorem

Front

Back

F(x): Concavity

Front

If f`` is positive, then f` is increasing, and the concavity of f(x) is upwards If f`` is negative, then f` is decreasing, and the concavity of f(x) is downwards

Back

Differentiation: Quotient Rule

Front

Back

Fundamental Theorem of Calculus

Front

Back

Integration: Natural Logarithm

Front

(squiggly line antiderivative)d/du = ln|u| + C

Back

Differentiation: Chain Rule

Front

Back

MVT for Integrals

Front

Back

dy/dx

Front

Back

Definite Integral

Front

Back

Volumes of Solids of Revolution

Front

Rotating the the region between two curves about a line, then finding the volume created

Back

Absolute Max./Min.

Front

Only occur at critical points or end points of a continuous function (guaranteed by the EVT)

Back

Washer Volume along x axis

Front

Back

Related Rates

Front

Suppose two variables, each a function of "time", are related by an equation. 1. Differentiate both sides of the equation 2. Use data given for variables and on of the rates to solve for the other rate

Back

Cylindrical Shell Volume

Front

h = R-r

Back

Differentiation: Power Rule

Front

Back

Second Fundamental Theorem of Calculus

Front

Back

Integration: Exponential Function

Front

Back

Numerical Differentiation

Front

Used to estimate the derivative (F(x+h)-f(x))/h

Back

Mean Value Theorem

Front

Back

F(x): Increasing or Decreasing

Front

If f`is positive, then f(x) is increasing If f` is negative, then f(x) is decreasing

Back

Area Between Curves

Front

Back

Integration: Power Rule

Front

Back

Differentiation: Inverse Functions

Front

Back

Finding Average Velocity

Front

Back

Differentiation: Trig Functions

Front

Back

Extreme Value Theorem

Front

There must be a max and min if the function is continuous on [a,b]

Back