436 Answered Questions for the topic Calculus 2

03/13/16

limits of integration
In geometry, you learn that the volume of a cylinder is given by V = πr2h, where r is the radius and h is the height of the cylinder. Use integration in cylindrical coordinates to confirm the... more
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03/13/16

Evaluate the integral below.
Evaluate the integral below.   ∫_0^1¦∫_y^(2−y)¦ ∫_0^(2−x−y)¦ xy dz dx dy    
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03/13/16

Evaluate the integral below given R. (Hint: what is the upper boundary of x?)
Evaluate the integral below given R. (Hint: what is the upper boundary of x?)     ∫∫1_R^  xy daR bounded byx=0y=0y=9−x^2      
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03/13/16

Find the integral below.
Find the integral below.       ∫∫1_R^ (x+2y) dar={(x, y):0≤x≤3, 1≤y≤4}    
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Calculus 2 Calculus Calculus 3

03/05/16

Given the function below and point P, what is the direction of the steepest ascent?
Given the function below and point P, what is the direction of the steepest ascent?   f(x)=x^2−4y^2−9
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Calculus 2 Calculus Calculus 3

03/05/16

Plot the function below.
Plot the function below.     f(x,y)=sin x cos y
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02/16/16

Convert the following polar equation to Cartesian coordinates.
Convert the following polar equation to Cartesian coordinates.   r=8 sin 0
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02/16/16

Find dy/dx ??
Given the parametric equations x = f(t) and y = g(t), dy/dx is given by g'(t)/f'(t). Find dy/dx given parametric equations below.   dy/dx=(g^′ (t))/(f^′ (t) )   Parametric... more
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02/16/16

Convert the following polar coordinates to Cartesian coordinates.
Convert the following polar coordinates to Cartesian coordinates.   (3,pi/4)
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02/16/16

Plot the parametric equations???
Plot the parametric equations below.   x=6 cos t y=4 sin t
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Calculus 2 Calculus Calc Calculus 1

02/15/16

Migratory birds fly north past a check-point at 300-300cos(pi(t)/6) birds per month. t= number of months since the beginning of the year.
A. Find the total number of birds for the year. B. When are the birds migrating the fastest. C. When is the migratory rate increasing the fastest?
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Calculus 2 Calculus Calculus 3

02/07/16

Which convergence test???
Which convergence test(s) would you use to determine the convergence of the series below?   ∑_(i=0)^∞  (i+3)/i!
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Calculus 2 Calculus 3 Calculus 1

02/07/16

converges or diverges ??
Explain why the series below Explain why the series below converges or diverges using the p-series test.      ∑_(i=1)^∞  1/i^3
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Calculus 2 Calculus Calculus 3

02/07/16

Evaluate the geometric series below?
Evaluate the geometric series below.   ∑_(i=0)^∞  12(4/7)^i
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02/04/16

Evaluate the finite series below.
∑_(i=1)^4¦(i−1)!/t^2
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02/04/16

terms and sequences
List the first 6 terms of the sequence below.   (−1)^(n−1)/2n
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Calculus 2

02/02/16

how to integrate e^(-5x/7) from -7 to infinity?is it finite or infinite?if so than why?
i see that this graph goes to infinity at -2 and horizontally it starts from 2.so its indefinite i guess but whats the reason for that.
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Calculus 2 Math Calculus Calculus 3

01/31/16

Find the volume of the solid generated???
Let R be the region bounded by two curves described below. Find the volume of the solid generated when R is revolved about the x-axis.       y=2x y=16 4√x
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Calculus 2 Math Calculus Calculus 1

01/31/16

How much work is required to move an object horizontally???
The definition of work, W, done by a force F in moving an object from point a to point b is given below. How much work is required to move an object horizontally from a = 1 m to b = 3 m by force... more
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Calculus 2 Math Calculus Calculus 1

01/31/16

area bound by y and the x-axis?
What is the area bound by y and the x-axis?   y=2 sin2x
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Calculus 2 Math Calculus Calculus 1

01/31/16

indefinite integral??
Find the indefinite integral below.   ∫(x^(3/4)+x^(5/2) )dx
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Calculus 2 Math

01/31/16

speed and velocity question
An baseball travels horizontally with a velocity v below. How far does it roll between t = 0 and t = 4 seconds?   v(t)=2t+5
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Calculus 2

01/07/16

Maclaurin series for e^x and Riemann sum
Find the Maclaurin series using e¹ for the lim n->∞ nsin(2πen!):The Maclaurin series for e×=1+x+x²/2!+x³/3!+...=∑x^k/k! as k goes from 0 to ∞. Time=Distance/Rate.Is the Maclaurin series for e×... more
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Calculus 2

12/15/15

Find all 4 intersection points of the graphs r=1+cos? and r=1+sin(2?)
Find all 4 intersection points of the graphs r=1+cosθ and r=1+sin(2θ).
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12/13/15

calculus function
You can perform calculus on functions with several variables. For example, you now know how to find limits of functions with a single variable and are able to extend the knowledge to functions of... more
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