Limits
Differentiation
Integration
Logs & Exponential & Transcendental Functions
Others
100
Limit technique where you multiply by the conjugate
What is Rationalize?
100
4
what is the derivative of 4x?
100
The area under the graph
What are integrals used to solve?
100
ea+b
what is an alternative way to write eaeb?
100
Use the area of a trapezoid to get approximation of area under curve.
what is the Trapezoid rule?
200
Limit rule used when you get 0/0
What is L'Hopital's Rule?
200
f'(x) is increasing
f''(x) is greater than 0
when is f concave up?
200
Velocity
what is the integral of acceleration?
200
eab
what is an alternative to (ea)b?
200
1. set U to equal inner function.
2. find du/dx.
3. solve for dx.
4. plug into integrate.
5. integrate new problem.
What is the substitution rule?
300
what theorem state that if lim X->9 P(x)=9 &
lim X->9 K(x)=9 & P(x)<M(x)<K(x) therefore M(x)=9
What is Squeeze Theorem?
300
33x2+2x+1
what is the derivative 11x3+x2+x?
300
2x2+c
what is the integral of 4x?
300
1. Equation containing derivatives.
2. solution has no derivatives.
3. general solution has +c while particular doesn't
What is a differential equation?
300
Johann Bernoulli.
Who invented L'Hôpital's rule?
400
1. f(x) is defined
2. limx->c f(x) exists
3.limx->c f(x)=f(c)
How do you know a function is continuous?
400
Theorem that states that the tangent line is parallel to secant line & instantaneous rate is equal to average rate of change.
what is mean value theorem?
400
ln|secx+tanx|+c
what is the integral of secx?
400
1. graphically represents differential equation
2. gives a visual of curve that solves the differential equation
What are slope fields?
400
f(b)-f(a) / b-a
What is mean value theorem?
500
1. limx->c- f(x) = limits coming from negative side
2. limx->c+ f(x) = limits coming from positive side
3. limx->c =L & limx->c- f(x) = limx->c+ f(x)
What are One-Sided limits?
500
Cusp
What part of this graph destroys differentiation?
500
1/a arctan(u/a)+c
what is the integral of du * 1/ a2+u2
500
k is constant of proportionality
what is K in direct variation?
500
f is defined at c.
If f'(c)=0
If f(x) is not differential at c.
What are critical #s