Definitions
If the function is not continuous at a point x = a
What is discontinuity?
The integral of x2
What is x3/3 +C?
d/dx(sinx)
What is cosx?
if a function is continuous on a closed interval [a,b], then the function must have a maximum and a minimum on the interval
What is Extreme Value Theorem?
What method would you use to solve this problem
Two cars start out 500 miles apart. Car A is to the west of Car B and starts driving to the east (i.e. towards Car B) at 35 mph and at the same time Car B starts driving south at 50 mph. After 3 hours of driving at what rate is the distance between the two cars changing
What is Rate of change?
As x approaches a of f(x) = L if and only if we can make the values of f(x) arbitrarily close to L (as close as we like) by taking x to be sufficiently close to a (on either side) but not equal to a
What is limit?
The integral of 1/x
What is ln absolute value of x +C?
d/dx(tanx)
What is sec2?
If the function f(x) is continuous on [a, b], AND the first derivative exists on the interval (a, b), then there is at least one number x = c in (a, b) such that f'(c) = [f(b) - f(a)]/(b-a) .
What is Mean Value Theorem?
Calculus the study of
What is Continuous Change?
The rate of change of a function's derivative
What is concavity?
The integral ln x
What is xln(x)-x+C?
d/dx(cscx)
What is -cscxcotx?
Integral between [a,b] of f(x)dx = F(b) - F(a) where F'(x) = f(x)
What is the Fundamental Theorem of Calculus?
D/dx [f(u)] = f '(u)du/dx OR dy/dx = (dy/du)(du/dx)
What is the Chain Rule?
The instantaneous rate of change of a function with respect to one of its variables.
What is derivative?
The integral of 5x
What is 5x/ln(5) + C?
d/dx(secx)
What is sec(x)tan(x)?
If f is a real-valued continuous function on the interval [a, b], and u is a number between f(a) and f(b), then there is a c ∈ [a, b] such that f(c) = u.
What is the Intermediate Value Theorem?
Who created Calculus
What is Issac Newton and Gottfried Leibniz
The point in which the rate of change of slope from increasing to decreasing manner or vice versa.
What is inflection point?
integral of cos 2(5x)
What is 1/2(x + sin(10x)/10) + C?
d/dx(cotx)
What is -csc2(x)?
If the function f(x) is continuous on [a, b], AND the first derivative exists on the interval (a, b), AND f(a) = f(b), then there is at least one number x = c in (a, b) such that f'(c) = 0.
What is Rolle's Theorem?
What does calculus mean in latin
What is Pebble?