Exam 2: Limits and the Derivative

Find the equation of the tangent line to the curve when x has the given value. -Find the equation of the tangent line to the graph of the function at the given value of x.

Provide an appropriate response. -Use a sign chart to solve the inequality. Express answers in interval notation.

Solve the problem. -V = 43 πr3, where r is the radius, in centimeters. By approximately how much does the volume of a sphere increase when the radius is increased from 1.0 cm to 1.1 cm?

Provide an appropriate response. -Use a graphing utility to find the discontinuities of the given rational function.

Provide an appropriate response. -Find

Provide an appropriate response. -Suppose that the total profit in hundreds of dollars from selling x items is given by Find the marginal profit at x = 5.

Use the definition to find the derivative at x. -

Provide an appropriate response. -Find the equation of the tangent line at x = 2 for . Write the answer in the form y = mx + b.

Provide an appropriate response. -A spherical balloon is being inflated. Find the approximate change in volume if the radius increases from 6.1 cm to 6.3 cm.

The graph of y = f(x) is shown. Use the graph to answer the question. -

Find the limit, if it exists. -Given

Provide an appropriate response. -Find

Provide an appropriate response. -Find the equation of the tangent line at . Write the answer in the form y = mx + b.

Provide an appropriate response. -Let f and g be functions that satisfy . Find h'(4) for .

The graph of y = f(x) is shown. Use the graph to answer the question. -

Provide an appropriate response. -Use the four step process to find for the function

Provide an appropriate response. -Find

Find dy. -

Use the given graph to find the indicated limit. -

Provide an appropriate response. -If the limit at infinity exists, find the limit.