Exam 11: Limits: A Preview to Calculus

Find the limit, if it exists.

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

Find the limit by using limit laws and special limits.

The gas mileage (miles per gallon, mpg) for a typical sedan can be approximated by the quadratic function , where x represents the speed of the car in miles per hour (mph) and f represents the gas mileage in mpg. Find the instantaneous rate of change of the gas mileage of this sedan when the speed is 68 mph.

Find the limit, if it exists.

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

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. on ; four rectangles with right endpoints

Find the limit, if it exists.

Find the limit, if it exists.

Find the limit, if it exists.

Find the limit of the summation.

Find the limit by using limit laws and special limits.

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

Evaluate the one-sided limits in order to find the limit, if it exists.

Find the derivative of f '(x).

Approximate the area under the curve (between the graph of f, the x-axis, x = 0 and x = 3) using 6 rectangles and using right endpoints.

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

Find the limit, if it exists.

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