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151 day 18 April 9, 2015
What is calculus? study of change
Increasing concave up ,Increasing concave down, decreasing concave up, decreasing concave down
average v. instantaneous
limits bring two points to one
derivative is slope of tangent line
definition of derivative
Quick rules (lnx)'= 1/x (e^x)'=e^x
(sinx)'= cosx (cosx)'=sinx
(sinhx)'= coshx (coshx)'=sinhx
Theorems
1. Mean Value
2. Intermediate Value
3. Squeeze
Continuity and Limits
4. Fundamental Theorem of Calculus
151 day 18 April 9, 2015
Rules:
power, product, quotient, chain rule
implicit differentiation
logarithmic differation
related rates
differentials error, linearizing a funtion
Newtons method
l'hopitals 0 * oo
curve sketching
Optimization
optimization
Main Idea
constraint
find the shortest distance from (1, 2) to the parabola y = 9 x^2
Main idea: D2(x,y) = ( x 1 )2 + ( y 2)2
constraint: 9 x2
D2(x) = ( x 1 )2 + ( 9 x2 2)2
151 day 18 April 9, 2015
Integration
F(x) = antiderivative of f(x)
F'(x) = f(x)
x2 + C = antiderivative of 2x
cos(x) dx = sinx + C
sin(x) dx = cosx + C
ln x + C
domain x not 0 for both sides
151 day 18 April 9, 2015
power Rule for integration
constant rule
sum rule
(f + g)dx fdx + gdx
x2 3x + 7 dx
x2 3x + 7 dx
151 day 18 April 9, 2015
Connect Rule
why is this so hard?
151 day 18 April 9, 2015
151 day 18 April 9, 2015
Fundamental Theorem
Relates Antiderivative with area under a curve
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