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Theorems
Trigonometric Functions
Limits
Integrals/Derivatives
Misc.
100
If f(x) is continuous and differentiable on the interval (a,b) and f(a)=f(b), there must be some point on (a,b) where f'(x)=0.
What is Rolle's Theorem?
100
∫sinx dx =
What is -cos x?
100
The value a function approaches as the variable approaches some point.
What is a limit?
100
d/dx [f(g(x))] = f'(g(x))*g'(x)
What is the chain rule?
100
A line perpendicular to the tangent line
What is a normal line?
200
If f(x) is continuous and diffferentiable, there is an x-value, c, where f'(c) equals the slope of the tangent lines through the endpoints
What is the Mean Value Theorem?
200
The derivative of tan x
What is sec²x ?
200
a. f(c) is defined b. the limit as x approaches c exists c. the limit as x approaches c = f(c)
What are the conditions of continuity?
200
A method for determining the Maximum or Minimum of a function
What is the first derivative test?
200
ln(e)
What is 1?
300
F(x)= ∫ f(t) dt F'(x) = f(t)
What is the Fundamental Theorem of Calculus?
300
The derivative of cos x
What is -sin x?
300
TRUE or FALSE If a function f is not defined at x = a then the limit, lim f(x) as x approaches a, never exists.
What is false?
300
∫ acceleration dt or d/dx [ position ]
What is velocity?
300
d/dx [ ln(u) ]
What is u'/u
400
If f(x) is continuous on (a,b) and f(a)= -5 and f(b)=2 then we can conclude that there is some x-value,c, where f(x)=0
What is the Intermediate Value Theorem?
400
The derivative of sec x
What is sec x tan x?
400
If a graph increases or decreases without bound, it is said to have a(n) ___________ limit.
What is infinite?
400
(pi)∫ R² - r² dx , from x=a to x=b
What is the Washer Method?
500
if f(x) is continuous on the closed interval [a,b] then it must attain a maximum and minimum at least once.
What is the Extreme Value Theorem?
500
∫ -csc²x
What is cot x?
500
a. f(x) approaches a different number from the right of c than it approaches from the left b. f(x) increases or decreases without bound as x approaches c c. f(x) oscillates between two fixed values as x approaches c
What are the cases where a limit fails to exist?
500
An approximation of the area of a region, often the region underneath a curve, using rectangles and an integral equation.
What is a Rienmann Sum?
500
A pebble is dropped into a calm pond, causing ripples in the form of concentric circles. The radius, r, of the outer ripple is increasing at a constant rate of 1 foot per second. When the radius is 4 feet, at what rate is the total area, A, of the disturbed water changing?
What is 8 pi ft²/s