Limits
Continuity
Derivatives
Implicit / Applications
Potpourri
100
This of f(x), as x approaches a, equals L. You make the values of f(x) arbitrarily close to L by taking x to be sufficiently close to a, on both sides of a, but not equal to a.
What is a limit?
100
lim x-> a f(x) = f(a) In other words, a function is said to be this at a number a, if the limit as x approaches a is equal to f(x) evaluated at a.
What is continuous?
100
This is equal to the slope of the function
What is a derivative?
100
The slope of the velocity / time graph
What is the acceleration graph?
100
This is a technique for finding a maximum or minimum value of a function, of several variables, subject to a set of constraints.
What is optimization?
200
This type of limit as x approaches a, from either the right or left, is equal to L if you can make the values of f(x) arbitrarily close to L by taking x to be sufficiently close to a, and x less than a. Also known as left or right-handed limits.
What is a one-sided limit?
200
- The limit of f(x) exists - The limit as x approaches a of f(x) equals f(a) - And the function is defined, in other words is inside the domain of f
What are the requirements for continuity?
200
• cf = c*f' • x^n = nx^(n-1) • f + g = f’ + g’ • f - g = f’ − g’ • f*g = f*g’ + f’*g • f/g = (f’*g − g’*f )/g^2 • f º g = (f’ º g) * g’ • f(g(x)) = f’(g(x))g’(x) • dy/dx = dy/du * du/dx • lnx = 1/x • a^x = a^x * ln(a) • e^x = e^x
What are derivative rules?
200
A more specified format of the chain rule; it is the process of finding the derivative of a dependent variable by differentiating each term separately
What is implicit differentiation?
200
This is finding a rate at which a quantity changes by relating that quantity to other quantities whose rates of change are known. The rate of change is usually with respect to time.
What is related rates?
300
This type of limit as x approaches a, from either the right or left, can be made arbitrarily large (as large as you please), by taking x sufficiently close to a, but not equal to a.
What is an infinite limit?
300
This states that a function is continuous from a direction if the limit as x approaches a from the direction is equal to f(a)
What is directional continuity?
300
sinx = cosx cosx = -sinx tan = sec^2x cscx = -cscx cotx secx = secx tanx cotx = -csc^2x
What are the trigonometric derivative rules?
300
This is the slope of the position / time graph.
What is the velocity graph?
300
This is extremely stupid.
What is history?
400
This type of limit appears in the form infinity over infinity, 0 over 0, 0 minus 0, or infinity minus infinity. The limit must be forced to these values.
What is an indeterminate limit?
400
This is continuous at every number inside an interval a to b.
What is a function that is continuous on its interval?
400
sin^-1(x) = 1/√(1−x^2) cos^-1(x) = −1/√(1−x2) tan^-1(x) = 1/(1+x2)
What are the inverse trigonometric rules?
400
This is represented by the variable 's' and its second derivative is the acceleration graph
What is position graph?
400
The phrase "Let them eat cake" is commonly attributed to this person.
Who is Queen Marie Antoinette?
500
When the limit is in an indeterminate form, infinity over infinity or zero over zero, this rule states you can take the limit of derivative of the numerator divided by the derivative of the denominator.
What is L'Hospital's Rule?
500
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What is poj;oih
500
f'(a) = lim h -> 0 (f(a+h) - f(a))/h
What is the formal definition of a derivative?
500
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What is udavhufhweu
500
This person is credited with inventing the first mechanical computer.
Who is Charles Babbage?
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