Questions from General Calculus

Q: Differentiate the following functions. y = ln (x2 +

Differentiate the following functions. y = ln (x2 + 1) /(x2 + 1)

Q: Find the second derivatives. d2/dt2 (t2 ln

Find the second derivatives. d2/dt2 (t2 ln t)

Q: Find the second derivatives. d2/dt2 ln(ln

Find the second derivatives. d2/dt2 ln(ln t)

Q: Use the fact that at the beginning of 1998, the population

Use the fact that at the beginning of 1998, the population of the United States was 268,924,000 people and growing at the rate of 1,856,000 people per year. At the beginning of 1998, the annual per ca...

Q: The graph of f (x) = (ln x)/√

The graph of f (x) = (ln x)/√x is shown in Fig. 4. Find the coordinates of the maximum point. Figure 4:

Q: The graph of f (x) = x/(ln x

The graph of f (x) = x/(ln x + x) is shown in Fig. 5. Find the coordinates of the minimum point. Figure 5:

Q: The following function may be viewed as a composite function h (

The following function may be viewed as a composite function h (x) = f ( g (x)). Find f (x) and g (x). h(x) = (5x2 + 1)-1/2

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

Write the equation of the tangent line to the graph of y = ln(x2 + e) at x = 0.

Q: The function f (x) = (ln x + 1

The function f (x) = (ln x + 1)>x has a relative extreme point for x > 0. Find the coordinates of the point. Is it a relative maximum point?

Q: Determine the domain of definition of the given function. (

Determine the domain of definition of the given function. (a) f (t) = ln(ln t) (b) f (t) = ln(ln(ln t))