04/28/13

Find the limit?
Find lim as (x, y)--->(0, 0) for (8x^2*y^2)/(x^4+y^4). lim as (0, y)--->(0, 0) =0/y^4=0 lim as (x, 0)--->(0, 0) =0/x^4=0 The limit is 0, right? But doesn't exist is the answer for this... more
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04/27/13

Let aT be the tangential component of the acceleration?
Let aT be the tangential component of the acceleration vector of r(t)=<t-sin(t), 1-cos(t), 0>. What is (aT)^2 at t=pi/2? r'(t)=<1-cos(t), sin(t), 0> r''(t)=<sin(t), cos(t),... more
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04/26/13

Let a=<2, 3, 1> and b=<-2, 5, -3>?
Let a=<2, 3, 1> and b=<-2, 5, -3>. Find the absolute value of a+b.  
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04/25/13

Find the curvature of the curve of intersection?
Find the curvature of the curve of intersection of the cylinder x^2+y^2=16 and the plane x+z=5 at (4, 0, 1).  
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04/25/13

Find the Cartesian equation for the curve?
Find the Cartesian equation for the curve described by the polar equation r=1/(1-sin(theta)).
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04/25/13

What is the y-component of r(pi/2)?
If r'(t)=<sin(t), -cos(t), 2t> and r(0)=<1, 1, 2>. What is the y-component of r(pi/2)? r(t)=<-cos(t), -sin(t), t^2> r(pi/2)=-1 So -1 is the answer?
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04/24/13

Let k(x) be the curvature of y=ln(x) at x.
Let k(x) be the curvature of y=ln(x) at x. Find the limit as x approaches to the positive infinity of k(x).
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04/23/13

Find the domain of r(t)?
Find the domain of r(t)=<sqrt(t^2), 1/(t-1), ln(t+1)>. Answer: (-1, 1)U(1, positive infinity) But how do you figure this out?
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04/23/13

Find the curvature of the curve?
Find the curvature of the curve r(t)=(t+1)i+2(t^2-1)j+(t-2)k. r'(t)=i+4tj+k sqrt(1^2+(4t)^2+1^2)=sqrt(2+16t^2) r''(t)=4j r'(t)xr''(t)=? Please show your work step by step from here to get the... more
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04/22/13

What's f(x, -x^2, x^2)?
If f(x, y, z)=(z^2+x^2-y)/(2x^2+y), what's f(x, -x^2, x^2)? Answer: x^2+2 I have no idea to do this.
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04/22/13

What's the arc length for the curve?
What's the arc length for the curve defined by r(t)=3sin(t)i+3cos(t)j+4tk for 0<=t<=10? (Answer: 50) r'(t)=<3cost, -3sint, 4>  
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04/21/13

Determine the minimum surface area?
Determine the minimum surface area of a closed rectangular box with volume 8 ft^3.
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04/21/13

Find the shortest distance between the planes?
Find the shortest distance between the planes 2x+3y-z=2 and 2x+3y-z=4.
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04/19/13

If f(x, y, z)=sin(3x-yz)?
If f(x, y, z)=sin(3x-yz), where x=e^(t-1), y=t^3, z=t-2, what's df/dt(1)? df/dt=(df/dx)(dx/dt)+(df/dy)(dy/dt)+(df/dz)(dz/dt) (3cos(3x-yz))(e^(t-1))+(cos(3x-z))(3t^2) +(cos(3x-y))(1) What should... more
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04/15/13

If f(x, y, z)=sin(3x-yz), where x=e^(t-1),?
If f(x, y, z)=sin(3x-yz), where x=e^(t-1), y=t^3, z=t-2, what's df/dt(1)?
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04/15/13

What's the length of the curve?
What's the length of the curve r(t)=<2 cos t, 2 sin t, sqrt(5)> from 0<=t<=2pi?
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04/14/13

True or False? The integral from 0 to 2pi?
True or False? The integral from 0 to 2pi, from 0 to 4, from r to 4 dz dr dtheta represents the volume enclosed by the cone z=sqrt(x^2+y^2) and the plane z=4.
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04/13/13

Use Stokes' Theorem to evaluate the surface integral?
Use Stokes' Theorem to evaluate the surface integral where F=<zx^2, z(e^xy^2)-x, x*ln (y^2)> and where S is the portion of z=1-x^2-y^2 above the xy-plane with n upward. Answer:... more
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04/09/13

Use Stokes' Theorem to evaluate the line integral?
Use Stokes' Theorem to evaluate the line integral where F=<(x^2)(e^x)-y, sqrt(y^2+1), z^3> and where C is the boundary of the portion of z=4-x^2-y^2 above the xy-plane. The curl is <0, 0,... more
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04/08/13

Show that the limit does not exist?
Show that lim (x, y)-->(0, 0) (3x^2(y))/(x^4+y^2) does not exist.
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04/07/13

Find the directional derivative of f(x, y)?
Find the directional derivative of f(x, y)=x^2*y+4y^2 at (2, 1) for u=<1/2, sqrt(3)/2>. Answer: 2+6sqrt(3) <2xy, 8y> at (2, 1)=<4, 8> <4, 8>*<1/2,... more
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04/07/13

Find the directional derivative?
Find the directional derivative of f(x, y)=x^2*y+4y^2 at (2, 1) for u=<1/2, sqrt(3)/2>. Answer: 2+6sqrt(3) The gradient is <2xy, 8y> at (2, 1)=<4, 8> And <4, 8>*<1/2,... more
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04/07/13

Find the gradient of f(x, y)?
Find the gradient of f(x, y)=2e^4x/y-2x at (2, -1). Answer: <-8e^-8-2, -16e^-8> Step by step, I really don't know this completely.
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04/06/13

Find the gradient of f(x, y)?
Find the gradient of f(x, y)=xe^xy^2+cosy^2. Answer: <e^xy^2+xy^2*e^xy^2, 2x^2*y*e^xy^2-2ysiny^2>
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04/06/13

Use implicit differentiation to find dz/dx and dz/dy?
Use implicit differentiation to find dz/dx and dz/dy for 3x^2*z+2z^3-3yz=0. Answer: dz/dx=-6xz/(3x^2+6z^2-3y) dz/dy=3z/(3x^2+6z^2-3y) This is Calculus 3 topic. Show your work through steps.
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