Questions from General Calculus

Q: Use logarithmic differentiation to find the derivative of the function.

Use logarithmic differentiation to find the derivative of the function. y = x cos x

Q: If g(x) = x/ex, find g

If g(x) = x/ex, find g(n)(x).

Q: Small birds like finches alternate between flapping their wings and keeping them

Small birds like finches alternate between flapping their wings and keeping them folded while gliding (see Figure 1). In this project we analyze this phenomenon and try to determine how frequently a b...

Q: Reduce the equation to one of the standard forms, classify the

Reduce the equation to one of the standard forms, classify the surface, and sketch it. x2 + y2 - 2x - 6y - z + 10 = 0

Q: (a) How is the number e defined? (

(a) How is the number e defined? (b) Use a calculator to estimate the values of the limits correct to two decimal places. What can you conclude about the value of e?

Q: Find the work done by a force F = 8 i -

Find the work done by a force F = 8 i - 6 j + 9k that moves an object from the point (0, 10, 8) to the point (6, 12, 20) along a straight line. The distance is measured in meters and the force in newt...

Q: Find |u × v | and determine whether u × v

Find |u × v | and determine whether u × v is directed into the page or out of the page.

Q: The figure shows a vector a in the xy-plane and

The figure shows a vector a in the xy-plane and a vector b in the direction of k. Their lengths are |a | = 3 and |b | = 2. (a). Find |a × b |. (b). Use the right-hand rule to decide wh...

Q: Find a formula for f (n)(x) if f

Find a formula for f (n)(x) if f (x) = ln(x - 1).

Q: Prove the property of cross products (Theorem 11). Property

Prove the property of cross products (Theorem 11). Property 4: (a + b) × c = a × c + b × c