Questions from Calculus

Q: Find an equation of the tangent plane to the given surface at

Find an equation of the tangent plane to the given surface at the specified point. z = (x + 2)2 – 2 (y – 1)2 - 5, (2, 3, 3)

Q: Find an equation of the tangent plane to the given surface at

Find an equation of the tangent plane to the given surface at the specified point. z = ex-y, (2, 2, 1)

Q: Find an equation of the tangent plane to the given surface at

Find an equation of the tangent plane to the given surface at the specified point. z = x/y2, (-4, 2, -1)

Q: Find an equation of the tangent plane to the given surface at

Find an equation of the tangent plane to the given surface at the specified point. z = x sin (x + y), (-1, 1, 0)

Q: (a). How do you find the velocity, speed,

(a). How do you find the velocity, speed, and acceleration of a particle that moves along a space curve? (b). Write the acceleration in terms of its tangential and normal components

Q: Find the velocity and position vectors of a particle that has the

Find the velocity and position vectors of a particle that has the given acceleration and the given initial velocity and position. a(t) = 2 i + 2t k, v (0) = 3 i - j, r (0) = j + k

Q: State Kepler’s Laws.

State Kepler’s Laws.

Q: (a). Write formulas for the unit normal and binormal vectors

(a). Write formulas for the unit normal and binormal vectors of a smooth space curve r(t). (b). What is the normal plane of a curve at a point? What is the osculating plane? What is the osculating cir...

Q: Find parametric equations for the tangent line to the curve x =

Find parametric equations for the tangent line to the curve x = 2 sin t, y = 2 sin 2t , z = 2 sin 3t at the point (1, 3 , 2). Graph the curve and the tangent line on a common screen.

Q: Let C be the curve with equations x = 2 - t3

Let C be the curve with equations x = 2 - t3, y = 2t - 1, z − ln t. Find (a). the point where C intersects the xz-plane, (b). parametric equations of the tangent line at (1, 1, 0), and (c). an equati...