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Calculus concept map

Derivation

Derivation

Derivative

Instantaneous Rate of Change

Slope

lim f(x1+delta x)-f(x1)/delta x

average rate of change: delta y/delta x

instantaneous rate of change: lim (delta y/delta x)

Discontinuity

Point

Jump

Infinite are undefined derivative because

f (c)= DNE

Limit

lim f(x)=L

Approach

Limit and continuity

Def: the function is contunues.

f(c) is defined

lim f(x) exists

Discontinuity:

jump

point

infinite

Continuity

Techniques of Limit

Techniques

Constant K

Sum Rule

Difference Rule

Product Rule

Quotient Rule

Power Rule

Techniques of differentiation

(detrivative)

Techniques

Derivative of a Constant

Power Rule

Constant Multiple Rule

Sum/Difference Rule

Product Rule

Quotient Rule

Chain Rule

Chain Rule

Chain rule

First derivative

Second derivative

Implicit differentiation

Implicit

x and y mixed together

To find dy/dx, take d/dx each side of equation, and simplify

Application

Extreme Value

L'Hoptial's rule

Minima and maxima

Extreme Value

Local Maxima: f(c) is an abs min for some open interval containing

Local Minima: f(c)is an abs max for same open interval containing

L'Hopital rule

lim f(x)/g(x)=lim f'(x)/g'(x)

f and g are diff'able functions and

f(a)=g(a)=0

Integral

Integration

Method of retrieving function from wihch a given derivative came

Techniques

17 Integrals

Integration by Parts

Parts

Solve Trigonometric integral

Trigonometric

Use substitution

Separate Sine or cosine

Integrate with Substitution

Substitution

substitution

Applications

Area between two curves

Volumes of revolution

Cylindrical shells

Area between two curves

Area

Volume of revolution

Volumes

Cylindrical Shells

Cylindrical

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