Exam 1: Functions, graphs, and Limits

​Approximate the critical numbers of the function shown in the graph and determine whether the function has a relative maximum,a relative minimum,an absolute maximum,an absolute minimum,or none of these at each critical number on the interval shown. ​ ​

​Simplify the expression using the given function definition. ​ ​ , ​

​Find the derivative of the following function. ​ ​

​A function and its graph are given.Use the graph to find the vertical asymptotes,if they exist.Confirm your results analytically. ​ ​ ​ ​ ​

​Find the slope m and y-intercept b of the line whose equation is given below. ​ ​

​Locate the absolute extrema of the function on the closed interval ​

​Differentiate the given function. ​ ​ ​

​Write the exponential equation as a logarithmic equation.

​A rancher has 440 feet of fencing to enclose two adjacent rectangular corrals (see figure).What dimensions should be used so that the enclosed area will be a maximum? ​ ​ ​

​Assume that x and y are differentiable functions of t.Find given that , ,and ​ ​

Find ​ ​ ​

​Complete the table and use the result to estimate the limit.Round your answer to six decimal places. ​ ​ ​

​Use the given information to write an exponential equation for y.Does the function represent exponential growth or exponential decay? ​ ,when

​Find ​ ​ ​

A graph of is shown and a c-value is given.For this problem,use the graph to find ​ ​ ​ ​

​Match the function with one of the following graphs. ​

The effective yield is the annual rate i that will produce the same interest per year as the nominal rate compounded n times per year.For a rate that is compounded n times per year,the formula for effective yield is given as Find the effective yield for a nominal rate of 9%,compounded monthly.Round your answer to two decimal places. ​

Find the slope m and y-intercept b of the line whose equation is given below. ​ ​

​Sketch the graph of the function ​

​Find ,if ​