Exam 2: Functions, Limits and the Derivative

Let Find the derivative of . __________ Find the equation of the tangent line to the curve at the point . __________ Select the correct graph of by answering A, B, or C.__________

Determine whether the equation defines y as a linear function of x.If so, write it in the form y = mx + b. X = 5y - 25

Determine whether the given function is a polynomial function or rational function.State the degree, if it is a polynomial function.

Let h be the function defined by . Find h(8), h(0), h(a) and h( a).

In a certain state, the sales tax T on the amount of taxable goods is 1% of the value of the goods purchased (x), where both T and x are measured in dollars.Express T as a function of x.

A function f is continuous at the point if the following conditions are satisfied. 1. is defined. 2) exists. 3) . Determine the values of x, if any, at which the function is discontinuous.At each point of discontinuity, state the condition(s) for continuity that are violated.

Find of the functions.

For the pair of supply and demand equations, where x represents the quantity demanded in thousands of units and p the unit price in dollars, find the equilibrium quantity and the equilibrium price. and __________ units $ __________

Evaluate h (3), where Round the answer to two decimal places, if necessary h (3) = __________

Find f (a + h) - f (a) for the function f (x) = 2x + 4.Simplify your answer.

Let , .Find the rule for the function f - g.

For the supply equation where x is the quantity supplied in units of a thousand and p is the unit price in dollars, determine the price at which the supplier will make 2 units of the commodity available in the market. $__________

Use the graph of the function f to find and if the limit exists.If it does not, answer none. __________ __________ __________

Find the domain of the function

Find the indicated limit, if it exists.

Determine whether the given function is a polynomial function or rational function.State the degree, if it is a polynomial function.

Use the graph of the given function f to determine at the indicated value of a. __________

Find the limit, if it exists.

At a temperature of , the volume V (in liters) of 1.33 g of is related to its pressure p (in atmospheres) by the formula . What is the average rate of change of V with respect to p as p increases from to ? What is the rate of change of V with respect to p when

Let f be the function defined by f (x) = 4x + 8. Find f (1), f (- 1), f (a), f (- a), and f (a + 1).