Questions from General Calculus

Q: If f is a differentiable function such that f (x)

If f is a differentiable function such that f (x) is never 0 and fx0 f (t) dt = [f (x)]2 for all x, find f.

Q: Estimate the area of the region enclosed by the loop of the

Estimate the area of the region enclosed by the loop of the curve x = t3 -12t, y = 3t2 + 2t + 5.

Q: Find the point on the parabola y = 1 – x2 at

Find the point on the parabola y = 1 – x2 at which the tangent line cuts from the first quadrant the triangle with the smallest area.

Q: Evaluate limx→o = 1/x fx0(1 –

Evaluate limx→o = 1/x fx0(1 – tan 2t)1/t, dt.

Q: A circular disk of radius is used in an evaporator and is

A circular disk of radius is used in an evaporator and is rotated in a vertical plane. If it is to be partially submerged in the liquid so as to maximize the exposed wetted area of the disk, show that...

Q: Use Part 1 of the Fundamental Theorem of Calculus to find the

Use Part 1 of the Fundamental Theorem of Calculus to find the derivative of the function.

Q: A curve is defined by the parametric equations Find the length of

A curve is defined by the parametric equations Find the length of the arc of the curve from the origin to the nearest point where there is a vertical tangent line.

Q: Let f (x) be the probability density function for the

Let f (x) be the probability density function for the lifetime of a manufacturer’s highest quality car tire, where is measured in miles. Explain the meaning of each integral.

Q: Let f (t) be the probability density function for the

Let f (t) be the probability density function for the time it takes you to drive to school in the morning, where t is measured in minutes. Express the following probabilities as integrals. (a). The pr...

Q: Let f (x) = 3/64 x √16

Let f (x) = 3/64 x √16 – x2, for 0 < x < 4 and f (x) = 0 for all other values of x. (a). Verify that f is a probability density function. (b). Find P (X < 2).