Calculus Answers

Find the domain and range and sketch the graph of the function f(x)= sqrt 16+6x-x²

A man drives from Detroit to Chicago, say 300 mi., at an average speed of 60 mi. per hr., stops

1 hr. in Chicago, and returns at a speed of 50 mi. per hour. Neglecting variations of speed en-route:

Write formulas expressing x (distance from Detroit) as a function of t.

If F(t) = 4t^2i - tj + t^2k and G(t) = ti + 2t^2j + 4 sin t k, then find (cos t F)

If F(t) = 4t^2i - tj + t^2k and G(t) = ti + 2t^2j + 4 sin t k, then find d/dt (F*G)

An object in free fall from

50 m high, so the height is

when t is h(t) = 50 – 4.9t2

.

What is the speed at

t = 2?

2. Determine the equation of the tangent line

on the curve y = x3 at the point (2.8)

An object in free fall from

50 m high, so the height is

when t is h(t) = 50 – 4.9t2

.

What is the speed at

t = 2?

2. Determine the equation of the tangent line

on the curve y = x3 at the point (2.8)

f'(x) of f(x) = 2x^2 + 8x = 10

Q.1: Apply Gauss's Divergence theorem to evaluate double integration S (lx^ 2 +my^ 2 +nz^ 2 )dS taken over the sphere (x-a)^ 2 +(y-b)^ 2 +(z-c)^ 2 = rho^ 2 ;l,m,n being the direction cosines of the external normal to the sphere.