***Please read the questions carefully***** 1.) Find the equation of the tangent

Question

***Please read the questions carefully*****

1.)   Find the equation of the tangent plane to the surface z = e^(-1x/17) ln(3y)

         at the point (-3, 2, 2.138)?

2.)  Find the linearization L (x, y) of the function F(x, y) = sqrt(301 - 16x^2 - 4y^2) at (-4, 3)?

3.)  Consider the ellipsoid 2x^2 + 5y^2 + z^2 = 26

      

a.)  The implicit form of the tangent plane to this ellipsoid at (1, -2, -2) is?

b.)  The parametric form of the line through this point that is perpendicular to that tangent  plane is L(t) =?

4.)  Find the linearization of the function F (x, y) = sqrt (83 - 3x^2 - 4y^2) at the point (5, 1)

   a.) L (x, y) = ?

    b.) Use the linear approximation to estimate the value of F (4.9, 1, 1)

5.) The radius of a right circular cone is increasing at a rate of 2 inches per second and its height is decreasing at a rate of 2 inches per second. At what rate is the volume of the cone changing when the radius is 40 inches and the height is 10 inches?

Note: (The answer has to be in "cubic inches per second)

Note: (The answer has to be in "amperes per second")

****Please show full show and write eligible for points to be awarded.

  And all the questions must be answered correctly to receive points.

If you can't answer all the questions, please don't expect me to award you the points.

Thanks.

Find the equation of the tangent plane to the surface z = e^(-1x/17) ln(3y) at the point (-3, 2, 2.138)? Find the linearization L (x, y) of the function F(x, y) = sqrt(301 - 16x^2 - 4y^2) at (-4, 3)? Consider the ellipsoid 2x^2 + 5y^2 + z^2 = 26 The implicit form of the tangent plane to this ellipsoid at (1, -2, -2) is? The parametric form of the line through this point that is perpendicular to that tangent plane is L(t) =? Find the linearization of the function F (x, y) = sqrt (83 - 3x^2 - 4y^2) at the point (5, 1) L (x, y) = ? Use the linear approximation to estimate the value of F (4.9, 1, 1) The radius of a right circular cone is increasing at a rate of 2 inches per second and its height is decreasing at a rate of 2 inches per second. At what rate is the volume of the cone changing when the radius is 40 inches and the height is 10 inches? Note: (The answer has to be in "cubic inches per second) In a simple electric circuit, Ohm's law states that , where V is the voltage in volts, I is the current in amperes, and R is the resistance in ohms. Assume that, as the battery wears out, the voltage decreases at 0.04 volts per second and, as the resistor heats up, the resistance is increasing at 0.02 ohms per second. When the resistance is 100 ohms and the current is 0.04 amperes, at what rate is the current changing? Note: (The answer has to be in "amperes per second") ****Please show full show and write eligible for points to be awarded. And all the questions must be answered correctly to receive points. If you can't answer all the questions, please don't expect me to award you the points.

Explanation / Answer

6

V = IR
dV/dt = R dI/dt + I dR/dt
dV/dt = -.01
R = 100: dR/dt = .01
I = .03 amps

dI/dt = (dV/dt - I dR/dt)/R = (-.01- (.03)(.01))/100 =-0.000103 amps/s

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