154. The linearization of log₃x
a. Find the linearization of
f(x) = log₃xatx = 3.
Then round its coefficients to two decimal places.

82. Use the definitions of the hyperbolic functions to find each of the following limits.

a. lim(x→∞) tanh x

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)

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?

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

1. Which of the following functions grow faster than e^x as x→∞? Which grow at the same rate as e^x? Which grow slower?

a. x-3