Questions from General Calculus

Q: A sample of 8 grams of radioactive material is placed in a

A sample of 8 grams of radioactive material is placed in a vault. Let P(t) be the amount remaining after t years, and let P(t) satisfy the differential equation P(t) = -.021P(t). (a) Find the formula...

Q: Compute dy/dx using the chain rule in formula (1

Compute dy/dx using the chain rule in formula (1). State your answer in terms of x only. y = (u2 + 2u)/(u + 1), u = x(x + 1) Chain Rule:

Q: Compute dy/dt |t=t0. y =

Compute dy/dt |t=t0. y = x2 - 3x, x = t2 + 3, t0 = 0

Q: Differentiate the function. y = [(3x2 + 2x +

Differentiate the function. y = [(3x2 + 2x + 2)(x - 2)]2

Q: Compute dy/dt |t=t0. y =

Compute dy/dt |t=t0. y = (x2 - 2x + 4)2, x = 1/t + 1, t0 = 1

Q: Compute dy/dt |t=t0. y =

Compute dy/dt |t=t0. y = (x + 1)/(x – 1), x = t2/4, t0 = 3

Q: Compute dy/dt |t=t0. y =

Compute dy/dt |t=t0. y = √(x + 1), x = √(t + 1), t0 = 0

Q: Find the equation of the line tangent to the graph of y

Find the equation of the line tangent to the graph of y = 2x(x - 4)6 at the point (5, 10).

Q: Find the equation of the line tangent to the graph of y

Find the equation of the line tangent to the graph of y = x/(√2 - x2) at the point (1, 1).

Q: Find the x-coordinates of all points on the curve y

Find the x-coordinates of all points on the curve y = (-x2 + 4x - 3)3 with a horizontal tangent line.