# calc 3

Most popular questions
1. ## Calc 3

At what point on the paraboloid y = x2 + z2 is the tangent plane parallel to the plane 7x + 2y + 3z = 2? (If an answer does not exist, enter DNE.)

asked by Becky on September 27, 2012
2. ## Calc 3

Find all partial derivatives? v = (xy)/(x-y) vxx= vxy= vyx= vyy=

asked by Becky on September 20, 2012
3. ## calc 3

Use polar coordinates to find the limit. [If (r, θ) are polar coordinates of the point (x, y) with r ≥ 0, note that r → 0+ as (x, y) → (0, 0).] (If an answer does not exist, enter DNE.) lim (x, y)→(0, 0) [(3e^−x^2− y^2) − 3]/ (x^2 + y^2)

asked by Becky on September 17, 2012
4. ## calc 3

Use the Chain Rule to find dw/dt. w = ln (x^2 + y^2 + z^2)^.5 , x = 9 sin t, y = 6 cos t, z = 7 tan t

asked by Becky on September 20, 2012
5. ## Calc 3

Find parametric equations for the tangent line to the curve of intersection of the paraboloid z = x^2 + y^2 and the ellipsoid 6x^2 + 5y^2 + 7z^2 = 39 at the point (−1, 1, 2)

asked by Becky on September 28, 2012
6. ## Calc 3

Two ropes are attached to the bumper of a car. Rope A is pulled with a force of 60 pounds at an angle of 30° to the horizontal ground, and rope B is pulled with a force of 80 pounds at an angle of 15° to the horizontal ground. The same effect can be

asked by Mitchel on January 18, 2018
7. ## calc 3

The magnitude of a velocity vector is called speed. Suppose that a wind is blowing from the direction N45°W at a speed of 40 km/h. (This means that the direction from which the wind blows is 45° west of the northerly direction.) A pilot is steering a

asked by Becky on August 31, 2012
8. ## Calc 3

Find parametric equations for the tangent line to the curve of intersection of the paraboloid z = x2 + y2 and the ellipsoid 6x2 + 5y2 + 7z2 = 39 at the point (−1, 1, 2)

asked by Becky on September 27, 2012
9. ## Calc 3

Suppose you leave home and hike 10 miles due north, then 8 miles in the direction 40° east of north, and then 6 miles due east. (a) How far are you from home? (b) What direction should you hike in order to return home?

asked by Mitchel on January 18, 2018
10. ## calc 3

Find parametric equations for the tangent line to the curve of intersection of the paraboloid z = x2 + y2 and the ellipsoid 7x2 + 2y2 + 6z2 = 33 at the point (−1, 1, 2). (Enter your answer as a comma-separated list of equations. Let x, y, and z be in

asked by chinne on September 24, 2014
11. ## Calc 3

Jessica and Matthew are running toward the point P along the straight paths that make a fixed angle of θ (Figure 1). Suppose that Matthew runs with velocity va (m/s) and Jessica with velocity vb (m/s). Let f(x,y) be the distance from Matthew to Jessica

asked by ally on October 3, 2018
12. ## Calc 3

Let S be the square in the xy-plane, oriented with the normal pointing in the positive z-direction. Estimate ∬S F⋅dS where F is a vector field whose values at the labeled points are F(A)=⟨9,3,5⟩, F(C)=⟨9,8,−4⟩, F(B)=⟨−9,8,−7⟩,

asked by ally on April 16, 2019
13. ## Calc 3

The region W is the cone shown below. The angle at the vertex is 2π/3, and the top is flat and at a height of 5/sqrt(3). Write the limits of integration for ∫WdV in the following coordinates (do not reduce the domain of integration by taking advantage

asked by ally on March 26, 2019
14. ## Calc 3

Let C be the straight line curve between the points (0,5) and (1,0). Let N be the unit normal vector field on C, oriented so that it points away from the origin. Let F:R2→R2 be the vector field defined by F(x,y)=(x,11). Find the flux of F across the

asked by ally on April 5, 2019
15. ## Calc 3

Evaluate the line integral ∫5ydx+2xdy where C is the straight line path from (2,4) to (5,9).

asked by ally on April 4, 2019
16. ## Calc 3

Show that the projection into the xy-plane of the curve of intersection of the parabolic cylinder z=1−2y^2 and the paraboloid z=x^2+y^2 is an ellipse. Find a vector-parametric equation r→1(t)=⟨x(t),y(t),z(t)⟩ for the ellipse in the xy-plane.

asked by ally on January 29, 2019
17. ## Calc 3

Find the limit, if it exists. (If an answer does not exist, enter DNE.) lim (x, y)→(0, 0) of (x^2 + y^2)/[((x^2 + y^2 +64)^.5)-8]

asked by Becky on September 14, 2012
18. ## Calc 3

Find the volume of the wedge-shaped region contained in the cylinder x^2 + y^2 = 1 and bounded above by the plane z = x and below by the xy-plane. The picture is a cylinder with a diagonal plane through it creating a wedge. Thanks! ;)

asked by Alyssa on November 29, 2011
19. ## Calc 3

Find ∫CF⋅dr where C is a circle of radius 1 in the plane x+y+z=4, centered at (3,2,−1) and oriented clockwise when viewed from the origin, if F=4yi−3xj+3(y−x)k

asked by ally on April 23, 2019
20. ## Calc 3

Consider a piece of wire with uniform density. It is the quarter of a circle in the first quadrant. The circle is centered at the origin and has radius 3. Find the center of gravity (x¯,y¯) of the wire.

asked by ally on April 3, 2019
21. ## Calc 3

A wrench .9m long lies along the positive y-axis, and grips a bolt at the origin. A force is applied in the direction of (0,1,3) at the end of the wrench. Find the magnitude of the force in newtons needed to supply 100 J of torque to the bolt. This is the

asked by Raquel on September 13, 2007
22. ## Calc 3

Given the matrix A= a 6 5 a -8 8 7 9 a find all values of a that make |A|=0. Give your answer as a comma-separated list.

asked by ally on February 10, 2019
23. ## Calc 3

The DNA molecule has the shape of a double helix. The radius of each helix is about 10 angstroms (1 Å = 10−8 cm). Each helix rises about 34 Å during each complete turn, and there are about 2.9 × 108 complete turns. Estimate the length of each helix.

asked by Becky on October 10, 2012
24. ## Calc 3

Find the absolute maximum and absolute minimum of the function f(x,y)=2x^3+y^4 on the region {(x,y)|x^2+y^2≤25}.

asked by ally on February 23, 2019
25. ## Calc 3

Calculate the velocity and acceleration vectors, and speed for r(t)=⟨cos(6t),sin(t),sin(6t)⟩ when t=5π/6 .

asked by ally on February 1, 2019
26. ## Calc 3

A cooling tower for a nuclear reactor is to be constructed in the shape of a hyperboloid of one sheet. The diameter at the base is 300 m and the minimum diameter, 500 m above the base, is 200 m. Find an equation describing the shape of the tower in the

asked by Becky on September 12, 2012
27. ## Calc 3

Consider the points below. P(2, 0, 2), Q(−2, 1, 4), R(7, 2, 6) (a) Find a nonzero vector orthogonal to the plane through the points P, Q, and R. (b) Find the area of the triangle PQR. * I answered part a and got the correct answer with the vector I found

asked by Backy on September 8, 2012
28. ## Calc 3

Suppose F⃗(x,y)=⟨2y,−sin(y)⟩ and C is the circle of radius 9 centered at the origin oriented counterclockwise. Using your parametrization in part (a), set up an integral for calculating the circulation of F⃗ around C.

asked by ally on April 5, 2019
29. ## Calc 3

Let F⃗(x,y,z)=7x^2i⃗−sin(xy)(i⃗+j⃗). Calculate the divergence: div F→(x,y,z)=

asked by ally on April 10, 2019
30. ## Calc 3

Fine the contours f(x,y)= k for the k e {-1,0,1,2}. Plot these contour curves using solid line type. Clearly label the curves with the value of k. Hint: you must show the computation you used to recognize the contour curves.

asked by ally on March 11, 2019
31. ## Calc 3

Find the absolute maximum and minimum of the function f(x,y)=ysqrt(x)−y^2−x+3y on the domain 0≤x≤9, 0≤y≤6.

asked by ally on February 23, 2019
32. ## Calc 3

Find a parameterization for the curve (1,2) and (4,5). r(t)= where _

asked by ally on January 29, 2019
33. ## Calc 3

Find the critical point of the function f(x,y)=2e^x−4xe^y.

asked by ally on February 20, 2019
34. ## calc 3

Find the exact length of the curve. x = 1 + 9^t2, y = 7 + 6^t3, 0 ≤ t ≤ 2

asked by Tayb on January 18, 2018
35. ## Calc 3

Find the maximum and minimum values of the function f(x,y,z)=x+2y subject to the constraints y^2+z^2=225 and x+y+z=1. Maximum and minimum value is?

asked by ally on March 6, 2019
36. ## Calc 3

The oracle function f(x,y) is presented below. For each point (x,y) you enter the oracle will tell you the value f(x,y). Estimate the partial derivative of the function at (1.6,−0.0999999999999999) using the Newton quotient definition.

asked by ally on February 13, 2019
37. ## calc 3

1. Evaluate the given integral by making an appropriate change of variables, where R is the region in the first quadrant bounded by the ellipse 36x^2+25y^2=1. L= double integral R (4sin(144x^2+100y^2) dA. 2. Use the given transformation to evaluate the

asked by lala on November 4, 2014
38. ## Calc 3

The figure below shows some level curves of a differentiable function f(x,y). Based only on the information in the figure, estimate the directional derivative: fu⃗(3,1) where u→=(−i+j)/sqrt(2)

asked by ally on February 20, 2019
39. ## Calc 3

Perform the following operation: [ a 1-a [ 5 4 -1 1+a -a ] 3 -3 0 ] Note: The entries in the resulting matrix are functions of a.

asked by ally on February 10, 2019
40. ## calc 3

A cardboard box without a top is to have volume 500000 cubic cm. Find the dimensions which minimize the amount of material used. List them in ascending order.

asked by hanan on November 6, 2011
41. ## Calc 3

The plane containing the lines r1(t)=⟨1,−4,−1⟩+t⟨1,2,−2⟩ and r2(t)=⟨1,−4,−1⟩+t⟨1,0,3⟩ has scalar equation

asked by ally on September 11, 2018
42. ## calc 3

A woman walks due west on the deck of a ship at 4 mi/h. The ship is moving north at a speed of 15 mi/h. Find the speed and direction of the woman relative to the surface of the water. (Round your answers to one decimal place.)

asked by abby on September 1, 2012
43. ## calc 3

Find a unit vector that is parallel to the line tangent to the parabola y = x^2 at the point (4, 16).

asked by Tayb on August 25, 2017
44. ## Calc 3

Use the Chain Rule to find ∂z/∂s and ∂z/∂t. z = tan(u/v), u = 7s + 4t, v = 4s − 7t

asked by Becky on September 22, 2012
45. ## Calc 3

Find the parametric equations for the tangent line to the curve with the given parametric equations at specified point. x= e^t y=te^t z=te^(t^2) (1,0,0)

asked by Rebecca on November 10, 2010
46. ## Calc 3

Describe the locus of points in R3 equidistant from the origin (0, 0, 0), and the plane x + y + z = 1.

asked by James on February 8, 2018
47. ## Calc 3

Evaluate the surface integral S F · dS for the given vector field F and the oriented surface S. In other words, find the flux of F across S. For closed surfaces, use the positive (outward) orientation. F(x, y, z) = x i + y j + z4 k S is the part of the

asked by Anon on November 23, 2016
48. ## calc 3

Question Find an equation of the set of all points equidistant from the points A(−2, 5, 2) and B(5, 1, −3).

asked by Becky on August 30, 2012
49. ## calc 3

A pilot is flying a Cessna airplane at 180 mph (airspeed).He would like to fly in the direction N45W, but there is a 32 mph wind in the S60W direction.What direction should the pilot set his course for in order to fly along his desired track? What will his

asked by fernando on September 25, 2012
50. ## calc 3

The length script l, width w, and height h of a box change with time. At a certain instant the dimensions are script l = 7 m and w = h = 5 m, and script l and w are increasing at a rate of 6 m/s while h is decreasing at a rate of 4 m/s. At that instant

asked by Becky on September 21, 2012
51. ## Calc 3

Find the parametric equations for the tangent line to the curve with the given parametric equations at specified point. x= e^t y=te^t z=te^(t^2) (1,0,0)

asked by Rebecca on November 10, 2010
52. ## Calc 3

Compute the flux of the vector field v(x,y)=(x,y) across the circle around the origin of radius 3. Compute the flow of the vector field v(x,y)=(x,y) along the circle around the origin of radius 3. I know the equations to find flux and flow, but I don't

asked by Anon on December 2, 2015
53. ## Calc 3

If a function of one variable is continuous on an interval and has only one critical number, then a local maximum has to be an absolute maximum. But this is not true for functions of two variables. Show that the function f(x,y)= 3xe^y − x^3 − e^(3y

asked by Becky on October 1, 2012
54. ## Calc 3

If z = f(x, y), where x = r^2 + s^2 and y = 8rs, find ∂^2z/(∂r ∂s).

asked by Becky on September 22, 2012
55. ## Calc 3

intersect x^2+y^2=36-8x^2-8y^2

asked by Katie on July 13, 2011
56. ## calc 3

what is the y-particular of: y"-2y'+2y=(e^t)(sin(t))

asked by Michael on March 22, 2010
57. ## Calc 3

The actual span of the base of the dome is 143 feet. 1) Use cylindrical coordinates to write the surface of the dome as a function of the distance from the center of the base; that is find z = f (r) . 2) Use your function to find the height of the dome;

asked by joe on December 7, 2009
58. ## Calc 3

Find the distance from Q=(3,6,4) to the plane n ⋅⟨x,y,z⟩=2 where n=⟨3/5,4/5,0⟩. L=?

asked by ally on September 10, 2018
59. ## Calc 3

How do I integrate rcos2theta dr? and then I have to plug in the limits 1 and 2sin2theta for theta and plug what I get from that into a second integral. Help!

asked by Samantha on April 22, 2011
60. ## calc 3

find the arc length of the curve r(t)=

asked by ashley on September 24, 2010
61. ## Calc 3

What is the laplace transform of: f(t) = 0, 0

asked by Michael on February 26, 2010
62. ## Calc 3

Suppose xy^3z^2+133=2xy−z . Compute ∂z/∂x and ∂z/∂y at the point (2,−2,3).

asked by ally on October 3, 2018
63. ## Calc 3

The mass density at a given point of a thin wire is C is delta(x,y,z)=x. If C is parametrized by r(t)=, 0

asked by Anon on December 2, 2015
64. ## Calc 3

Let C be the intersection of x^2+y^2=16 and x+y+z=5. Find the curvature at (0,4,1). I don't know how to find the intersection between the given equations.

asked by Anon on October 15, 2015
65. ## calc 3

Find all partial derivatives? v = (xy)/(x-y) vxx= vxy= vyx= vyy=

asked by Becky on September 19, 2012
66. ## Calc 3

if r= and r_0= , describe the set of all points (x,y,z) such that magnitude[r-r_0]=4

asked by Emily on January 31, 2012
67. ## calc 3

Find the limit ( e^-3t i + tsin(1/t)j + arctan tk ) if it exists. If not say doesn’t exsist. (t→ ∞)

asked by rachel on September 20, 2010