True or False. A continuous function on a closed interval must attain a maximum value on that interval.
True
100
What is the integral, (6x^2-3)dx evaluatated
2x^3+3x+C
100
"Lo di high minus high di low all over lo lo"
What is this theorem?
Quotient rule
200
What is the derivative of tan(x)
sec(x)^2
200
What is the antiderivative of 1/2x
.5*ln(2x)+C
200
True or False. If u & v are differentiable functions then d(uv)=du*dv
False d(uv)=udv+vdu
200
What is the integral of (sec^2(x))dx
tan(x)+C
200
d/dx (f(x) g(x)) = f(x)g'(x) + g(x) f'(x)
What is this Theorem.
Product rule
300
What is the derivative of (sin(x))^2
2*cos(x)*sin(x)
300
What is the antiderivative of 4x^3+6x^2+24x
x^4+2x^3+12x^2+C
300
True or False. Any two solutions to the differential equation dy/dx=5 are parallel lines.
True since the slope is a constant, any two solutions have the same slope making them parallel.
300
Definite integrals find the values between the curve and the
...............
x-axis
300
If a real-valued function f is continuous in the closed and bounded interval [a,b], then f must attain its maximum and minimum value, each at least once. What is this theorem.
Extreme Value Theorem
400
What is the derivative of e^(x^3+5x^2+16x)
(3x^2+10x+16)*e^(x^3+5x^2+16x)
400
What is the antiderivative of 1/(1-x^2)^.5
arcsin+C
400
True or False if f"(c)=0 then (c,f(c)) is a point of inflection
False for example,consider f(x)=x^4 at c=0
400
A chemical flows into a storage tank at a rate of 180+3t liters per minute, where 0≤t≤60. Find the amount of the chemical that flows into the tank during the first 20 minutes.
4,200 liters of chemical flows into the storage tank each minute
400
There exists a point c in the interval (a,b) such that f'(c)=f(b)-f(a)/b-a, if a function is continuous on the closed interval [a,b] and differentiable on the open interval (a,b). What is this theorem
Mean Value Theorem
500
What is the derivative of x^3+8x+cos(3x)
3x^2+8-3sin(3x)
500
What is the antiderivative of sec³x*tanx
1/3sec^3(x)+C
500
True or False. If dy/dx=ky, then y=e^kx
False, y=Ce^kx
500
A particle is moving along a line so that its velocity is v(t0=tˆ3-10tˆ2+29t-20 ft/sec at time t. What is the displacement of the particle on the time interval 1≤t≤
32/3 ft
500
If f is continuous on an open interval containing a, then for every x in the interval the derivative of the the integral of f(x) dx on said interval is equal to f(x). What is this Theorem.