Limits & Continuity Questions and Answers

Consider the following functions f x x 8 g x x Find fog x Find the domain of fog x Enter your answer using interval notation Find gof x Find the domain of gof x Enter your answer using interval notation Find f of x Find the domain of fof x Enter your answer using interval notation Find analy

What is the sum of the first seven terms of the geometric series 3 12 48 192 O 4 372 O 12 288 O 16 383 O 65 535

a The formula for the sum of an infinite geometric series S 1 7 may be used to convert 0 23 to a fraction What the values of a and r a a 23 1 20 70 10 10 O 23 r 100 23 100 23 r 100

What is the sum of the geometric series 2 3 1 A 1 O 122 O 2 40 O 54

What is the solution to the equation 2x 4 12 20 O x 0 O x 1 Ox 2 O x 9

Which geometric series represents 0 4444 as a fraction O O 1 1 1 1 40 400 4 000 O 1 1 1 1 40 400 40 400 4 000 40 000 4 4 4 O 10 100 1 000 10 000 10 7 100 1 1 100 1 000 10 000

What is the true solution to the equation below 2log3 6x log3 4x 2log3 x 2 Ox 2 and x 1 Ox 2 and x 2 Ox 1 and x 4 x 2 and x 4 O

20 If x 3 is a factor of x 2x kx then k 13 x 1

et x asec in x a If a 0 and 0 B find sin and cos

2 Matt has some dimes and quarters in his pocket He has no other coins and the total value of his dimes equals the total value of his quarters What percentage of his coins are dimes Round answer to nearest percent

Use the Change of Base Formula to solve the equation for x Give an exact solution as a logarithm and an approximate solution rounded to the nearest thousand 4 5 The exact solution is x Type an exact answer

A woman borrowed 3900 from a bank for 6 months A friend was cosigner of the woman s personal note The bank collected 5 simple interest on the date of maturity a How much did the woman pay for the use of the money b Determine the amount she repaid to the bank on the due date of the note a The woman paid for the use of the money www

2 Show work You do not need to simplify your function Enclosing the Most Area with a Fence A farmer with 4000 meters of fencing wants to enclose a rectangular plot that borders on a river If the farmer does not fence the side along the river what is the largest area that can be enclosed See the figure 4000 2x 3 Solve show work and write the final answers in interval notation Show a 2D sketch of the gra or the number line with key points to help you find the solutions X 3x 10

Graph the solution set of the inequality where x is an x 9 015507

Evaluate the expression without using a calculator cos 30 sin 30

3 If f x x and g x 3 gof x 9 F09 x 13

Evaluate the following limits a lim 7m 4 OI LA

Complete the table below for each exponential function Use Interval Notation to define the Domain and Range Write intercepts as ordered pairs If an answer Does Not Exist write DNE y 100 3 y 800 0 9 Initial Value a Base b Domain Range Horizontal Intercept Vertical Intercept as a point Horizontal Asymptote Left to Right Behavior Select an answer 750 1 3 y Select an answer Select an answer

Suppose that as an 1 an n X 1 Find the radius O convergence sum n 1 infty a n 6 n x n

Write an equation for the polynomial graphed below 5 4 3 2 y 5 2 3 4 5 2 3 uit 5

the following inequality 3x 2 x 4 2 What is the solution Type your answer in interval notation Simplify your answer Use integers or fractions f

Write an equation for the polynomial graphed below 5 4 3 2 1 Th 5 4 3 2 2 3 4 5 2 3 4 5 y

5 4 3 n 2 T 2 What is the least possible degree of the polynomia graphed above

Find the lengths of the circular arc S 7 3 4 S

Find the radian measure of the angle with the given degree measure Round your answer to three decimal places 49 rad

A person s systolic blood pressure which is measured in millimeters of mercury mm Hg depends on a person s age in years The equation P 0 007y 0 01y 118 gives a person s blood pressure P at age y years A Find the systolic pressure to the nearest tenth of a millimeter for a person of age 43 years B If a person s systolic pressure is 135 mm Hg what is their age rounded to the nearest single year

Rewrite the expression 3 log x 2 log x 1 4 log x 1 as a single logarithm 3 log x x 1 4 2 1 2 X

Evaluating and Solving Rational Functions Gonzo and his friend Duke are heading out to San Diego on a road trip From Gonzo s front door to downtown San Diego the trip is 455 miles Answer the following questions based upon this situation Use the relationship Distance Rate times Time or d rt to write a rational function T r that has the rate of travel r in mph as its input and the time of travel in hours as its output 1 Solve the equation d rt for t What is the new equation d x syntax error this is not an equation syntax error Check your variables you might be using an incorrect one 2 Rewrite your new equation as a function where t T r and d 455 T r Determine the driving time to reach San Diego if Gonzo and Duke drive 90 miles per hour Round your answer to one decimal place If Gonzo and Duke drive 90 miles per hour the driving time for the trip will be about hours If it takes Gonzo and Duke 6 5 hours of driving time to reach San Diego determine how fast they drove If it takes Gonzo and Duke 6 5 hours of driving time to reach San Diego they drove about miles per hour Give the equation of the vertical asymptote of T r Vertical Asymptote Complete the following sentence to explain its significance in this situation

0 ans Find the horizontal asymptote of f x 7 x 7 3x 1 4 x 3x 2

Given 4 is a zero find the rest of the zeros of f x x 2x 10x 8 Enter the all of the zeros separated by commas Enter exact value not decimal approximations

Find the horizontal asymptote of f x y 7 x 7 3x 1 4 x 3x 2

Find the horizontal asymptote of f x y 5x 4x 5 2x x 4

A farmer needs to enclose three sides of a field with a fence the fourth side is a river The farmer has 42 yards of fence and wants the field to have an area of 208 sq yards What should the dimensions of the field be For the purpose of this problem the width will be the smaller dimension needing two sides the length with be the longer dimension needing one side Additionally the length should be as long as possible length yards width 13 x yards 16 hundredths

1 Homework C1S6 Question 1 of 9 1 point Question Attempt 1 of Unlin 2 3 9 8 7 6 5 4 3 2 Use translations to graph the given function n x x 1 16 80 SE 9 5 m 20 4 23 to 6 4 Da 5 a M

y 5x 6 2x y 3 give the coordinates of one point in

1 Part 0 2 2 Write an equation of the line that pas and in standard form Ax By C Part 1 of 2 3

Suppose that the function h is defined as follows h x 3 2 1 0 1 Graph the function h if 2 5 x 1 5 if 1 5 x 0 5 if 0 5 x 0 5 if 0 5 x 1 5 if 1 5 x 2 5 5 3 X

Simplify Write the answer using positive exponents 3 3 a 3 b 2 2 4 a 5 b 7

For the function T x do each of the following a Use the special trig limits in Section 3 3 to help you prove limx oT x 0 b Use the shortcut formulas of Chapter 3 so far to help you find T x You do NOT need to simplify your answer at all Bret

Cousin Throckmorton has gone into hiding to escape online publicity He has taken a room in a downtown hotel under the alias C and nervously reveals the room number to trusted family members only by telephoning them and playing a secret tone whose waveform reveals the curve y f x shown below Only you know that CT s room number is the 4 digit sequence b b b3b4 in which each digit b satisfies f x sin kx da k 1 2 3 4 Use the given information to find CT He is counting on you bk

Assignment 4 Problem 1 Previous Problem 1 point Let F be the function whose graph is shown below Evaluate eac f a limit does not exist or is undefined enter DNE 1 2 3 5 6 lim F x lim F x lim F x x 1 F 1 lim F x x 1 Problem List Next Problem lim F x x 1 3 1 0

roblem Problem List Next Prob ng limit represents the derivative of son and a

gnment 4 P Problem Problem List Find the value of the const

A line is going through points 1 2 and 1 6 Find slope of the line 02 03 2

28 cos 0 given cos 20 and 8 terminates in quadrant II 2

Find the vertical and horizontal asymptotes If none exist type none in the blank f x x 3 x 3x 18 Vertical Asymptote Horizontal Asymptote y

Graph the solution set of the inequality where x

Question 2 6 points Listen Using the graphs provided determine the equation for the polynomial function being represented Show all of your work a b 60 Y 54 48 42 36 30 24 18 12 6 2 6

7 Let x 0 Prove that the value of the following expression does no dt 1 14 16 2 Fully justify your ar 3 depend on x gument So 0 rx 1 73 1 dt 4 0 1 t 3

bof Question 1 GA 3 Part 1 of 2 Use the true conditional statement shown b statements as a biconditional If a number is positive then its cube r What is the converse of the given conditi citive then