1,131 Answered Questions for the topic AP Calculus

Ap Calculus Math Calculus Integral

08/15/15

solution of indefinite integral
What is a particular solution of the indefinite integral ∫(2)/(1-x2)dx that passes through (√3 , (Π/2)?   a) f(x)=√(3) tan-1x-(Π/6) b) f(x)=2tan-1x-(Π/6) c) f(x)=2tan-1x+√(3)
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Ap Calculus Math Calculus Ap Calc

08/15/15

find the general antiderivative of f(X)= 5/2x
a.) 5/2x2-C   b.) 5ln[2x]-C   c.) none of these %MCEPASTEBIN%
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Ap Calculus Calculus Ap Calc Calc

08/14/15

solving integral
∫ ( t/(√(2t2-1) )dt=________   A) (-1/2)(√(2t2-1))+C B) 4(√(2t2-1))+C C) 8(√(2t2-1)+C D) -( (1)/(4(2t2-1)) )+C E) (1/2)(√(2t2-1))+C  
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Ap Calculus Math Calculus Ap Calc

08/13/15

substituting in an integral
If the substitution √(X)=sin y is made in the integrand of: (top of the integral sign is (1/2), bottom of the sign is 0) ∫ ( √(X) )/( √(1-X) )dx, the resulting integral is_____________.   A.)... more
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Ap Calculus Calculus Integrals Ap Calc

08/12/15

solving integrals
∫( (du)/(u(u2-1)1/2) ) = __________________
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08/12/15

chain rule is also know as
The Chain Rule for antiderivatives is also known as the ___________________ rule.   -derivative -substitution -product -integral
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Ap Calculus Calculus Interval Ap Calc

08/12/15

find area under curve
Using the left-had approximation method with 5 equal subintervals, find the area under the curve f(x)=√(1+x3) on the interval [0,1].   a.) 1.074 b.) 1.156 c.) 2.356 d.) 1.110
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Ap Calculus Calculus Integrals Ap Calc

08/12/15

solving using integrals
if I have a graph of f(x) and I want to find (on the top of the integral sign is 5, and on the bottom is -2)  ∫f(x)dx   what would ∫f(x)dx equal?... (if the graph has points at (-5,2) (-2,0)... more
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Ap Calculus Calculus Integral

08/12/15

integrals for area between curves
what integral formula would represent the area between the curves f(x)=-x2+2x+3 and g(x)=x+1 on the interval [-1,2]?
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Ap Calculus Calculus Ap Calc Integral

08/12/15

solving integrals
∫ ( (dx)/√(x2+36) )=_____________     a. ( (√(x2+36)+x)/6 )+C   b. ln abs( (x+6)/(√(x2+36)) )+C   c. ln ( (√(x2+36)+x)/6 )+C      
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08/12/15

trigonometric substitution to evaluate integral
Which trigonometric substitution can be used  to evaluate the integral: ∫ ( (dx)/(√(a2+x2)) ) ...?   x= a tanθ   x=a sinθ   x=a secθ
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Ap Calculus Calculus Integrals Ap Calc

08/12/15

solving integrals
∫ ( (x+3)/√(1-x2) )dx=_____________
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Ap Calculus Calculus Ap Calc Calc

08/12/15

what is the antiderivative?
what would be the antiderivative of f(x)=12x3-9x2+8x-3   I believe it would be 3x4-3x3+4x2-3x+7 , is that correct?
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08/12/15

second derivatives
Using the second order derivative equation: ( (d2y)/(dx2) )-9y=o   Which of the following would be true?   y= e3x   y=e-3x   y=2e-3x   y=xe3x  
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08/11/15

substituting a value into an integrand
if the substitution √(x)=sin(y) is made into the integrand of (with the upper limit of: 1/2  and the lower limit of: 0) ∫ ( (√(x) )/( (√(1-x) )dx , the resulting integral is _______________.    
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Ap Calculus Calculus Integrals Calc

08/11/15

Word problem using rate of change and integrals
A giant spherical snowball is melting such that its radius decreases at a rate of 5 mm per hour. How fast is the surface area changing when the diameter is two meters? How fast is the volume... more
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Ap Calculus Calculus Tangent

08/11/15

find tangent and ppoints on curve where there is a horizontal or vertical tangent
If I have the equation x3+3xy2+y3=1   What would be the equation for the tangent line when x=0, and what are all the points on the curve where the curve has a horizontal or vertical tangent? (I... more
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08/11/15

continuous and differentiable function
Let f be a continous function on interval [-1, 9] and differentiable on (-1, 9).  If f(-1) = 2 and f(9) = 7, then which of the following are necessarily true?   i.   f'(c)= (1/2) for some c... more
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08/11/15

what is the absolute maximum
If f(x)= ((1/4)x4)+((1/3)x3)-(2x2)-(4x)+6 for x in the interval [–4,10], then f has an absolute maximum at ______.
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Ap Calculus Calculus

08/11/15

relative min and max
What is the total number of relative maximum and minimum points of the function whose derivative for all x is given by f ‘ (x) = x(x – 3)^2 (x + 1)^4 ?
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08/11/15

application of mean value theorem
The function f(x)= x(2/3)  on [-8,8] does not satisfy the conditions of the mean-value theorem because... A. f(0) is not defined.         B. f(x) is not continuous on [-8,8].              C. f ‘... more
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Ap Calculus

05/26/15

Find the area bounded by the curve x = y3 - 2y2 - 3y and the y-axis.
Calculus question that i am having trouble with
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Ap Calculus

02/24/15

The function f is continuous and non-linear for -3 is equal and less than x is equal and less than 7 and f(-3)=5 and f(7)=-5.
If there is no value of c on -3<x<7 for which f'(c)=-1, which of the following statements must be true? a) for come c on -3<c<7, f'(c)<-1 b) For some c on -3<c<7, f'(c)>-1... more
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Ap Calculus

01/04/15

whats the inverse of the function of y= 3x2 -2x +1
3x2 -2x +1
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11/23/14

double derivative y^3-xy=5 PLEASE HELP!!!
i just cant get why i got this wrong and i cant find the answer online, please tell me the answer and how to do this step by step, thank you so much!!
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