31. The incidence of a disease (Continuation of Example 4.) Suppose that in any given year the number of cases can be reduced by 25% instead of 20%.
a. How long will it take to reduce the number of cases to 1000?

6. Which of the following functions grow faster than ln(x) as x→∞? Which grow at the same rate as ln(x)? Which grow slower?

a. log_2(x²)

Use reference triangles in an appropriate quadrant to find the angles in Exercises 1–8.

3. a. arcsin(-1/2)

84.a. Find the center of mass of a thin plate of constant density covering the region between the curve y=1/√x and the x-axis from x=1 to x=16.

Find the inverse of the function f(x)=mx, where m is a constant different from zero.

143.

a. Show that ∫ ln(x) dx = x ln(x) − x + C.

154. The linearization of log₃x

a. Find the linearization of

f(x) = log₃xatx = 3.

Then round its coefficients to two decimal places.