Questions from General Calculus

Q: If f is a differentiable function and g(x) =

If f is a differentiable function and g(x) = xf(x), use the definition of a derivative to show that g’(x) = xf’(x) + f(x).

Q: Suppose f is a function that satisfies the equation f(

Suppose f is a function that satisfies the equation f(x + y) = f(x) + f(y) + x2y + xy2 for all real numbers x and y. Suppose also that a. Find f(0). b. Find f’(0). c. Find f&acir...

Q: Evaluate /

Evaluate

Q: Find numbers a and b such that /

Find numbers a and b such that

Q: Evaluate /

Evaluate

Q: Consider the function f(x) = tan/x.

Consider the function f(x) = tan/x. a. Show that f(x) = 0 for x = 1/Ï€ , 1/2Ï€, 1/3Ï€ , ... b. Show that f(x) = 1 for x = 4/Ï€ , 4/5Ï€ , 4/9Ï...

Q: The figure shows a point P on the parabola y = x2

The figure shows a point P on the parabola y = x2 and the point Q where the perpendicular bisector of OP intersects the y-axis. As P approaches the origin along the parabola, what happens to Q? Does i...

Q: Evaluate the following limits, if they exist, where [[x

Evaluate the following limits, if they exist, where [[x]] denotes the greatest integer function.

Q: Determine whether the statement is true or false. If it is

Determine whether the statement is true or false. If it is true, explain why. If it is false, explain why or give an example that disproves the statement. If limx→5 f(x) = 0 and limx → 5 g(x) = 0, th...

Q: Determine whether the statement is true or false. If it is

Determine whether the statement is true or false. If it is true, explain why. If it is false, explain why or give an example that disproves the statement. If neither limx → a f(x) nor limx → a g(x) ex...