Calculus and Above

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Hello, I need help with the...

Hello,

I need help with the following calculus problems:

1.) Sketch the curve = ; 0 less than or equal to t less than or equal to 2pi

2.) Find the arc length of the curve: r(t)=. Same constraints as above

3.) Find the intersection of the tangent line to the curve r(t)= at t=3pi/4 and the yz plane

4.) Find an equation of the normal plane to the curve r(t)= at t = 3pi/4

5.) If f(x,y,z)=(x^e)(y^pi)(e^z), evaluate gradient f(1,1,ln2)

6.) Find an equation of the tangent plane to the surface xsiny+ycosz=0 at (pi/2,pi/2,pi)

7.) Sketch the level curves to f(x,y)=y+sinx at levels -1,0, and 1

8.) Use the level curves of previous to sketch gradient f(0,0)

9.) Use gradients to show that the tangent line to the curve xy=1 at (1,1) is y=2-x

10.) Find the unit vector in the direction of steepest descending on the surface f(x,y)=250-1/4 (x^2)-3/4 (y^2) at (-1,1)

11.) Use Lagrange multiplier method to maximize z=(3x+15)y subject to x+y=91

I need help with the following calculus problems:

1.) Sketch the curve = ; 0 less than or equal to t less than or equal to 2pi

2.) Find the arc length of the curve: r(t)=. Same constraints as above

3.) Find the intersection of the tangent line to the curve r(t)= at t=3pi/4 and the yz plane

4.) Find an equation of the normal plane to the curve r(t)= at t = 3pi/4

5.) If f(x,y,z)=(x^e)(y^pi)(e^z), evaluate gradient f(1,1,ln2)

6.) Find an equation of the tangent plane to the surface xsiny+ycosz=0 at (pi/2,pi/2,pi)

7.) Sketch the level curves to f(x,y)=y+sinx at levels -1,0, and 1

8.) Use the level curves of previous to sketch gradient f(0,0)

9.) Use gradients to show that the tangent line to the curve xy=1 at (1,1) is y=2-x

10.) Find the unit vector in the direction of steepest descending on the surface f(x,y)=250-1/4 (x^2)-3/4 (y^2) at (-1,1)

11.) Use Lagrange multiplier method to maximize z=(3x+15)y subject to x+y=91

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