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330 Answered Questions for the topic Calculus 2

Calculus 2

05/01/16

Determine if the given function y=f(x) is a solution of the accompanying differential equation.

y=ex+4xex, y'-y=4ex

05/01/16

Set up an intefral for the length of the curve.

y=3cos(x), 0≤x≤pi
Calculus 2

04/30/16

Assist with answers and working out.

a) Show that 1/r(r+1) =1/r - 1/r+1   hence, show that (the sum from r=1 to n)  ∑ 1/r(r+!) = 1 - 1/n+1                           deduce that Sn the sum to infinity, if it exists.     b) The... more
Calculus 2

04/29/16

help with this math question

A series has sum Sn =n(2n-1) i) find, in terms of n, the nth term of the series. ii) Hence, show that the series is an AP   c. Find an expression for the sum to infinity of the Geometric... more
Calculus 2

04/23/16

the water from a fire hose follows a path described by y = 2.0+ 0.9x - 0.3x^2 (units are in meters).

 if v sub x is constant at 10 m/s find the resultant velocity at point (3.0,2.0) first question is what is the magnitude of the velocity?
Calculus 2 Calculus Calculus 3

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    
Calculus 2 Calculus Calculus 3

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
Calculus 2 Calculus Calculus 3

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
Calculus 2 Calculus Calculus 3

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
Calculus 2 Calculus Calculus 3

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)
Calculus 2 Calculus Calculus 3

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
Calculus 2 Calculus Calculus 3

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
Calculus 2 Calculus Calculus 3

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
Calculus 2 Calculus Pre Calculus

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
Calculus 2 Calculus Limits

03/17/16

Find the limit below.

Find the limit below.   limτ(x→3) (x^4−81)/(x−3)    
Calculus 2 Calculus Calculus 3

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.
Calculus 2 Calculus Calculus 3

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)
Calculus 2 Calculus Calculus 3

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)
Calculus 2 Calculus Calculus 3

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
Calculus 2 Calculus Calculus 3

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
Calculus 2 Calculus Integrals

03/13/16

Evaluate the integral below.

Evaluate the integral below.   ∫_0^1¦∫_y^(2−y)¦ ∫_0^(2−x−y)¦ xy dz dx dy    
Calculus 2 Calculus Integral

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      

03/13/16

Find the integral below.

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