Exam 2: Limits and Continuity

Courier rates for delivery of mail up to 200 g are given in the following chart: Draw the graph of the cost (in dollars) of mailing a letter as a function of its mass (in grams). Where are the discontinuities of this function? Is the cost function right or left continuous at these points?

In the following figure the curve is the graph of a quantity y that is a function of time t. Also shown is its tangent line at t = 100. What is the average rate of change of y from t = 20 to t = 160? What is the approximate rate of change of y with respect to t at t = 100?

Evaluate .

Let f(x) = and g(x) = 14 - . Compute .

If h(x) = if x $\neq$ 1 and h(1) = 4, then h is continuous at every x.

Let f(x) be defined by f(x) = Where, if anywhere, is f discontinuous?

Evaluate .

Let f(x) = Which of the following statements is true?

Evaluate . sin x

For what values of the constants c and k is the functionf(x) = continuous at all x?

Evaluate the following limit: x + .

Let f(x) = and g(x) = - 2. Which of the following is true?

To the nearest 1/1,000, how close need x be chosen to 1 to ensure that | - 1| < ?

Given that = 1, evaluate (5 + 7x - 3) sin .

Let g(x) = where k is a constant real number. If g has a removable discontinuity at x = 2, then k is equal to:

Evaluate .

Evaluate .

Evaluate .

Is the function f(x) = discontinuous at any point of its domain? Would your answer change if we also define f(3) = 6?

Evaluate .