Questions from General Calculus

Q: The value V of a machine t years after it is purchased

The value V of a machine t years after it is purchased is inversely proportional to the square root of t + 1. The initial value of the machine is $10,000. Write V as a function of t. Find the rate of...

Q: Consider the function f(x) = sin βx, where

Consider the function f(x) = sin βx, where β is a constant. Find the first-, second-, third-, and fourth-order derivatives of the function. Verify that the function and its second derivative satisfy t...

Q: Find the derivative of the function. g(x

Find the derivative of the function. g(x) = 3(4 – 9x)5/6

Q: Let f be a differentiable function of period p. Is

Let f be a differentiable function of period p. Is the function f′ periodic? Verify your answer. Consider the function g(x) = f(2x). Is the function g′(x) periodic? Verify your answer.

Q: Let r(x) = f(g(x))

Let r(x) = f(g(x)) and s(x) = g(f(x)), where f and g are shown in the figure. Find (a) r’(1) and (b) s’(4).

Q: Find the derivative of the function g(x) = sin2

Find the derivative of the function g(x) = sin2 x + cos2 x in two ways. For f(x) = sec2 x and g(x) = tan2 x, show that f’(x) = g’(x).

Q: Show that the derivative of an odd function is even. That

Show that the derivative of an odd function is even. That is, if (-x) = -f(x), then f’(-x) = f’(x). Show that the derivative of an even function is odd. That is, if (-x) = -f(x), then f’(-x) = f’(x)....

Q: Let u be a differentiable function of x. Use the fact

Let u be a differentiable function of x. Use the fact that

Q: g(x) = |3x - 5| Use

g(x) = |3x - 5| Use the result of Exercise 114 to find the derivative of the function.

Q: f(x) = |x2 - 9| Use

f(x) = |x2 - 9| Use the result of Exercise 114 to find the derivative of the function.