1,131 Answered Questions for the topic AP Calculus
If an object is displaced a distance d by a constant force F, the amount of work done is given by _____.
a. W=F+d
b. W=F-d
c. W=Fd
d. W=F/d
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Find the solution of the differential equation
equation: dy/dx=(x+1)/y2 that passes through the point (-2, 2).
a. y=√(1/2 x2+x+4) b. y=3√(3/2 x2 +2)
c. y=3√(3/2 x2+3x+8)
d. y=3√(1/2 x2+x+8)
e. none of these
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Equation to find the amount left after t years
Suppose that a sample initially contains N0 grams of a radioactive substance. If this substance has a half-life of 32 years, then which of the following equations can be used to find the amount...
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Which of these differential equations is NOT seperable?
dy/dy=x+y
dy/dy=xy
dy/dy=x/y
dy/dy=2xy
A tank is formed by revolving the graph of y=x^4 around the y-axis. The tank has a height of 16.
Find the value of m such that the line y = m represents the height at which the tank is half full.
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A solid has a flat base, which is bounded by the graph of y=x^3 and y=vx in the first quadrant only.fo
Each cross section of the solid perpendicular to the x-axis is the shape of a square.
Find the volume of this solid.a. 5/14 b. 25/126 c. 5/12 d. 47/125
Find the value of k on the interval...
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. Find the volume of the solid obtained by rotating the area bounded by y=sin x and the x-axis on the interval 0= x= 2? about the x-axis.
a. 5.490 b. 2.754 c. 10.912 d. 9.870
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Given a solid whose cross-section is defined by A(x), the volume of the solid is given by _____________________.
a) V=∫A'(x)dx
b) V=∫A(x)dx
c) V=Π∫A(x)dx
d)none of these
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Which of the following gives the volume of the solid created by revolving a curve f(x) around the y-axis?
V=2Π∫ xf(x)dx
V=Π∫ xf(x)dx
V=2Πx2f(x)dx
V=Π2∫ xf(x)dx
looking at a velocity time graph
when looking at a velocity vs. time graph, how can one determine the total distance traveled as well as the displacement?
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net change
the net change in y=f(x), as x changes from a to b is given by___________.
∫abs(F'(x)) dx
∫F'(x) dx
∫ abs(F(x)) dx
∫F(x) dx
none of these
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TRUE OR FALSE?
if f(x) is an even function,(above integral sign: 0 below integral sign: -a) ∫f(x)dx= (above integral sign: a below integral sign: 0) -∫f(x)dx true or false?
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which of the following integrals is INCORRECT?...
A) ∫tanxdx=sec2x+C
B) ∫cscxdx=ln[cscx-cotx]+C
C) ∫cotxdx=ln[sinx]+C
calculating area under curve
if you calculate the area under the curve f(x)=x2 from x=0 to x=5 using a left had rectangular approximation, a right hand approximation, and a midpoint rectangular approximation, in each case...
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integrating
when integrating ∫sin3xdx, a good first move would be to:
a) use u-substitution, letting u=sinx, and then integrating ∫u3du
b) use u-substitution, letting u=sin2x
c) rewrite the problem...
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dividing definite integrals
∫(top: b, bottom: a) ∫(f(x)/g(x))dx=(top: b, bottom: a)∫f(x)dx÷(top: b, bottom: a)∫g(x)dx
true or false?
definite integral
which of the following expressions are true about the definite integral of sinx on the interval [0,2Π]?
A) (top 2Π, bottom 0) ∫sinxdx= (Π →∞)lim (top: Π, bottom: i=0)∑sinxi 2Π
B) (top 2Π,...
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true or false?
y=e-x satisfies the differential equation, ( (d2y)/(dt2) )+y=0
true or false?
solution to differential equation
which of the following is a solution to the differential equation y''+2y'+y=0
a) y=cos2x
b) y=x2
c) y=xe-x
true or false?
y=sinx+cosx satisfies the differential equation ( (d2y)/(dt2) )+y=0
true or false?
true or false?
if f(x) is an even function,
(above integral sign: 0 below integral sign: -a) ∫f(x)dx= (above integral sign: a below integral sign: 0) -∫f(x)dx
true or false?
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which of the following is a solution of the differential equation dy/dx=y/x
a) y=2x
b) y=3x+2
c) y=ex
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