# calc 3

Most popular questions-
## 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* -
## Calc 3

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

*asked by Becky on September 20, 2012* -
## 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* -
## 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* -
## 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* -
## 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* -
## 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* -
## 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* -
## 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* -
## 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* -
## 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* -
## 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* -
## 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* -
## 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* -
## 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* -
## 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* -
## 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* -
## 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* -
## 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* -
## 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* -
## 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* -
## 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* -
## 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* -
## 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* -
## 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* -
## 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* -
## 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* -
## 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* -
## 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* -
## 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* -
## 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* -
## Calc 3

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

*asked by ally on January 29, 2019* -
## Calc 3

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

*asked by ally on February 20, 2019* -
## 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* -
## 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* -
## 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* -
## 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* -
## 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* -
## 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* -
## 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* -
## 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* -
## 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* -
## 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* -
## 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* -
## 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* -
## 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* -
## 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* -
## 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* -
## 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* -
## 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* -
## 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* -
## 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* -
## 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* -
## 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* -
## Calc 3

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

*asked by Katie on July 13, 2011* -
## calc 3

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

*asked by Michael on March 22, 2010* -
## 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* -
## 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* -
## 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* -
## calc 3

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

*asked by ashley on September 24, 2010* -
## Calc 3

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

*asked by Michael on February 26, 2010* -
## 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* -
## 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* -
## 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* -
## calc 3

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

*asked by Becky on September 19, 2012* -
## 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* -
## 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*