Exam 11: Limits: A Preview to Calculus

Use the graph to estimate the limit, if it exists. , where

Find the limit, if it exists.

Complete a table of values to four decimal places and use the result to estimate the limit.

If the profit function P(x) in dollars corresponding to producing x units is given by . Find the instantaneous rate of change of the profit when x = 113 units. Is the profit increasing or decreasing at 113 units? What is the meaning of P '(x) and what are its units?

Find the derivative of the f '(x).

Find the derivative of the function at the specified value of x.

Approximate the area under the curve using the given number of rectangles of equal width. Round your answer to 3 decimal places. on ; eight rectangles with leftendpoints

Find the derivative of f '(x).

For the graph of the function f shown, state the value of the given quantity.

Determine whether the sequence converges. If it does converge, state the limit.

Approximate the area under the curve (between the graph of f, the x-axis, x = 0 and x = 2) using 4 rectangles and using left endpoints.

Find the derivative of f '(x).

Find the equation of the tangent line to the graph of f at the given point. at the point

Calculate the work exerted when a man pushes with a force of pounds from x = 0 to x = 5 feet.

Find the derivative of the function at the specified value of x.

Evaluate the summation.

Given the graphs of the functions f and g, find the limit, if it exists.

Find the derivative of f '(x).

Find .

Find the slope of the tangent line to the graph of f at the given point. at the point