Questions from General Calculus

Q: Find the derivative of the vector function. /

Find the derivative of the vector function.

Q: Find the derivative of the vector function. r (t

Find the derivative of the vector function. r (t) = t2 i + cos (t2) j + sin2t k

Q: Find the derivative of the vector function. /

Find the derivative of the vector function.

Q: Find the length of the curve. r(t)

Find the length of the curve. r(t) = t2 i + 9t j + 4t3/2 k, 1 < t < 4

Q: Find the derivative of the vector function. r (t

Find the derivative of the vector function. r (t) = a + t b + t2 c

Q: Find the derivative of the vector function. r (t

Find the derivative of the vector function. r (t) = t a × (b + t c)

Q: Find the unit tangent vector T (t) at the point

Find the unit tangent vector T (t) at the point with the given value of the parameter t.

Q: Let C be the curve of intersection of the parabolic cylinder x2

Let C be the curve of intersection of the parabolic cylinder x2 = 2y and the surface 3z = xy. Find the exact length of C from the origin to the point (6, 18, 36).

Q: Find the unit tangent vector T (t) at the point

Find the unit tangent vector T (t) at the point with the given value of the parameter t. r (t) = cos t i + 3t j + 2 sin 2t k, t = 0

Q: Suppose you start at the point (0, 0, 3

Suppose you start at the point (0, 0, 3) and move 5 units along the curve x = 3 sin t, y = 4t, z = 3 cos t in the positive direction. Where are you now?