409 Answered Questions for the topic Calculus 2

03/18/16

Given the vectors below, carry out the operation.
Given the vectors below, carry out the operation.     u=(4, -2) v=(-4, 6 )   2u+3v    
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03/18/16

Plot the curve below and describe the picture in words.
Plot the curve below and describe the picture in words.       r=3 sin4θ
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03/18/16

What test would you use to determine whether the series below converges or diverges?
    ∑_(k=1)^∞ 1/k^(1+n) , n>0
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03/18/16

Using the disk method, find the volume of the solid generated by revolving about the x-axis the area bounded by the curves below.
Using the disk method, find the volume of the solid generated by revolving about the x-axis the area bounded by the curves below.   x=0 y=0 y=−2x+2
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03/18/16

Find the domain and the range of the function below.
Find the domain and the range of the function below.   g(y)=1/(y−2)
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03/17/16

Find a) the angle between u and v, b) projv u and c) scalv u. Recall that a ? b = |a||b| cos ?.
Find a) the angle between u and v, b) projv u and c) scalv u. Recall that a ? b = |a||b| cos θ.     u=-3i+4k v=-4i+j+5k
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03/17/16

The Cosine function is a Taylor series. Expand the series to 4 terms and use the result to approximate Cos (2p). How does the approximation compare to the actua
The Cosine function is a Taylor series. Expand the series to 4 terms and use the result to approximate Cos (2π). How does the approximation compare to the actual result? What would you need to get... more
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03/17/16

Using the disk method, find the volume of the solid generated by revolving about the x-axis the area bounded by the curves below.
Using the disk method, find the volume of the solid generated by revolving about the x-axis the area bounded by the curves below.     x=0 y=0 y=-2+2
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03/17/16

Calculate the area bounded by two curves below for x > 0.
Calculate the area bounded by two curves below for x > 0.       y=3xy=x^2
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03/17/16

Find the limit below.
Find the limit below.   limτ(x→3) (x^4−81)/(x−3)    
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03/15/16

Find the line integral below.
Find the line integral below.   ∫_c^ ¦(x−y+2z)ds where C is the circle r(t)=(1, 3 cost, 3 sin t) for 0≤t<2pi.
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03/15/16

Compute the curl of the vector field below.
Compute the curl of the vector field below.       F=(X^2-Z^2, 1, 2XZ)
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03/15/16

Find the divergence of the vector field below.
Find the divergence of the vector field below.       f =(X^2 YZ, -XY^2 Z, -XYZ^2)
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03/15/16

Find the gradient field of the potential function below.
Find the gradient field of the potential function below.       φ(x,y)=x^3+y+100
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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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