Questions from General Calculus

Q: Find h' in terms of f' and g'. h (

Find h' in terms of f' and g'. h (x) = f (g (sin 4x)

Q: At what point on the curve y = [ln (x

At what point on the curve y = [ln (x + 4)]2 is the tangent horizontal?

Q: Find the limit. limx→3 √x + 6

Find the limit. limx→3 √x + 6 – x/x3 - 3x2

Q: Graphs of the position functions of two particles are shown, where

Graphs of the position functions of two particles are shown, where is measured in seconds. When is each particle speeding up? When is it slowing down? Explain.

Q: Find equations of both lines that are tangent to the curve y

Find equations of both lines that are tangent to the curve y = 1 + x3 and parallel to the line 12x - y = 1.

Q: Find the points on the ellipse x2 + 2y2 = 1 where

Find the points on the ellipse x2 + 2y2 = 1 where the tangent line has slope 1.

Q: (a). On what interval is the function f (x

(a). On what interval is the function f (x) = (ln x)/x increasing? (b). On what interval f is concave upward?

Q: Find the limit. limx→π- ln (sinx

Find the limit. limx→π- ln (sinx)

Q: Find the limit. limx→-∞ 1 – 2x4 - x4

Find the limit. limx→-∞ 1 – 2x4 - x4/5 + x – 3x4

Q: An equation of motion of the form s = Ae-ct

An equation of motion of the form s = Ae-ct cos (ωt + δ) represents damped oscillation of an object. Find the velocity and acceleration of the object.