Find the Derivative of the given function at the indicated point.
f (x) = 1/x, a=2
What is -1/4
100
Find the Integral of x^3
What is x^4 /4
100
f(x)= x^3 +1 at [2,3]
What is 19
100
Integral of xsinx dx
What is -cosx + sinx + C
100
a of n = n/n+1 find 6th term and 50th term
What is 1/2, 2/3, 3/4, 4/5, 5/6, 6/7; 50/51
200
f'(a) = lim(x-->a) (f(x)-f(a))/(x-a)
find f'(x) if f(x)=3x-12
What is Limit Does Not Exist
200
The Trapezoidal Rule will underestimate Ing from a to bf(x) dx if the graph of f is concave up on [a,b]. True or False.
What is False. The Trapezoidal rule will overestimate the integral if the curve is concave up.
200
f(x) = e^x [-2,0]
What is 1-e^-2 /2 or approx 0.432
200
Integral of 3t e^2t dt
What is 3/2te^2t - 3/4e^2t + C
200
c of n = (1 + 1/n)^n
find the first six and 50th
What is 2, 9/4, 64/27, 626/256, 7776/3125, 117649/46656; (51/50)^50
300
Find the lines that are (a) tangent and (b) normal to the curve y=x^3 at the point (1,1).
What is (a) y=3x-2
(b) y=-1/3x + 4/3
300
What does the Integral find?
What is Area Under the Curve
300
y=x^2 at x=-2, (a) slope of the curve (b) tangent line (c) normal line USING LIMITS
What is (a) -4 (b) y=-4x-4 (c) y=1/4x + 9/2
300
Integral of x^2cosx dx
What is x^2sinx + 2xcosx - 2sinx + C
300
a of 1 = 3, a of n = a of n-1 - 2 for all n > or eq 2
find the first four and eighth term
What is 3, 1, -1, -3; -11
400
If f(2) =3 and f'(2)=5, find an equation of (a) the tangent line, and (b) the normal line to the graph of y=f(x) at the point where x=2
What is (a) y=5x-7 (b) y= -1/5x + 17/5
400
A particle starts at x=0 and moves along the x axis with velocity v(t) = 5 for time t>or eq to 0. where is the particle at t=4?
What is x=20
400
f(x)= |x| at x=2 find the slope
What is 1
400
Integral of 3x^2e^2x dx
What is 3/2x^2e^2x - 3/2xe^2x + 3/4e^2x + C
400
-2, 1, 4, 7... find the common difference, eight term, a recursive rule for the nth term, and an explicit rule for the nth term for the arithmetic series
What is 3, 19, a of n = a of n-1 + 3, a ofn 3n-5
500
f(x) = -x^2 + 3
What is dy/dx = -2x
500
A particle starts a x=0 and moves along the x axis with velocity v(t)=t^2 +1 for time t> or eq to 0. Where is the particle at t=4? Approximate the area under the curve using four rectangles of equal width and height determined by the midpoints of the intervals.
What is x=25
500
What is the rate of change of the area of a circle with respect to the radius when the radius is r=3 in?
What is 6pi in^2/in
500
Integral of y lny dy
What is y^2/2lny - y^2/4 +C
500
The second and fifth terms of an arithmetic series are -2 and 7 respectively. Find the first term and a recursive rule for the nth term.
What is -5, a of n = a of n-1 + 3 for all n> or equal to 2