Calclus

40 flashcards

Squeeze Thrm.: Squeez
IVT (Intermediate Value Thrm).: Is f(x) continuous on [x1,x2]?Is C value between f(x1) and f(x2)?
e^0: 1
Point Slope: y-y1=m(x-x1)
Horizontal Tangent Line: Slope of 0 and implies numerator is zero
When is a particle at rest: When velocity is zero
Vertical Tangent Line: Slope is undefined, implies denominator is zero
What is the derivative of f(y) where f is an unknown differentiable function of y: f'(y) * [dy/dx]
a^u like 3^(x^2): (a^u)(lna)(deriv of u)
Procedure for Related Rate Problems: 1. Draw Figure if necessary, and choose variables for all unknowns2. Write what is given and what is to be found using your variables and d?/dt symbols.3. Write equation relating with variables.3a) If a quantity is changing it must be represented with variable letter3b) If quantity is constant it must be represented with a number value.3c) Look for secondary relationship to reduce variables.4. Implicitly differentiate both sides with respect to t.5. Sub number values and solve6. Sentence.
Implicitly Differentiate: Differentiate both sides with respect to x.
How to find inverse of a function?: Swap x and y and solve for y.
x = sqrt9: 3
x^2 = 9: Plus or minus 3
What is the derivative of e^-x?: Chain Rule it,(e^-x)[-1]
How to find limit to infinity?: Divide the highest power term in the numerator by the highest power term in denominator.
When is the limit to infinity 0?: When there is a constant in the numerator and variable in the bottom, dividing by infinitely big or small goes closer to zero.
How to do piecewise continuous a and b problems?: Plug "breaking point" into each function, then make them equal to each other to test continuity
Velocity is what units?: Distance/time
Acceleration is what units: Distance/time^2
When is L'H applicable?: 0/0 and inf/inf
What functions have the slowest to fastest growth rate?: Constants and sin and cos (No growth), Logs, Power functions, Exponential functions
What does linear approximation mean?: Finding and using a tangent line from one point to approximate the y value at another point nearby.
How to find total distance?
How to find displacement?: Final position minus initial position
When is velocity increasing on an open interval?: When its acceleration is greater than zero
When is speed increasing on an open interval?: When velocity and acceleration have the same sign
EVT: If a function is continuous on [a,b] then it must have an abs max and abs min on the interval, found through candidate test
MVT: Test for continuity of closed interval and differentiablity of open intervals. If both are possible, find c by solving AROC=IROC
How do you get average velocity?: Displacement/elapsed time
How do you get average speed?: Total Displacement/elapsed time
How to find absolute global extrema?: Find critical numbers, the y value of critical numbers and at each endpoint of the interval, then select the least and greatest y-values as extrema. Draw a table.
What are critical numbers of f(x)?: X-values where f exists, but f' is zero or undefined
Where can absolute extrema occur?: At critical numbers or end points.
Where can relative extrema occur?: Only at critical numbers.
If the interval of a graph of f' is under the x-axis, what does that mean for the graph of f?: For that interval f has a negative slope and goes downward
What does it mean for a function to be monotonic on an interval?: It is only growing or shrinking continuously on an interval, meaning the derivative has the same sign on that interval.
The coordinates of relative minimums and maximums can be found with?: Critical Number=x and f(CN)=y
Quotiant rule is what and where do you use it?