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15 Cards in this Set

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How do you find an AVERAGE rate of change of a function f(x) on the interval [a,b]?
f(b)-f(a)/b-a
How do you find an instantaneous rate of change of a function f(x) at a point?
Find f'(x) and plug in the coordinates of the point.
How do you find the derivative using the limit process?
f'(x)=lim f(x+a)-f(x)/a
x-a
What are the rules for horizontal asymptotes?
If the degree on top is larger...then none.
If the degree on top is smaller....then zero.
If the degrees are the same on the top/bottom...then ratio of lead. coefficients.
What is removable discontinuity?
Describe analytically & graphically.
Analytically....you can remove common factors.
Graphically....there is a hole in the graph.
What is nonremovable discontinuity?
Describe analytically & graphically.
Analyticall....you cannot remove common factors.
Graphically....there is no way to make the function continuous (vertical asymptote, jump, oscilation.)
When does a limit exist?
When the limit from the right equals the limit from the left.
How do you find vertical asymptotes?
Factor the rational expression and look at the factors in the denominator. If no factors cancel with the numerator then the vertical asymptotes are the values of x that make the denominator equal to zero.
How do you find the slope of a normal line?
Find the slope of the tangent line and take the negative reciprocal.
What is displacement?
The change in position over time. (Delta s)
The antiderivative of velocity.
What is velocity?
The derivative of position or the antiderivative of acceleration.
What is acceleration?
The derivative of velocity.
How do you find total distance traveled when given a velocity function?
Integrate the absolute value of velocity.
How do you find the displacement of an object when given a velocity function?
Integrate the velocity function.
What is the process when differentiating implicitly?
1. Differentiate both sides with respect to x. (Remember to attach a y prime when differentiating y terms.)
2. Collect y prime terms on the left side of the equation.
3. Factor out y prime.
4. Solve for y prime.