Limits & Continuity Questions and Answers

Add in the indicated base 10123 10123 10123 10123

15 feet 15 feet inches inches Type a whole number or a decimal

60 inches 60 inches feet feet Type a whole number or a decimal

13 Write and use a piecewise function for this rental truck company Move to the Groove Trucking Flat Fee 100 Mileage First 50 mile FREE Additional miles 50 mile A f 10 B f 70 C Write a piecewise function that models the rental cost MOVING

An unfilled vacuum capacitor has a capacitance of 5 70mF It is then filled with a material with a dielectric constant of 2 20 What is the new capacitance of the capacitor 1 25 F 1 25x10 2 F 12 5 F 386 F 0 386 F 2 59 F 79 7 F 0 0797 F 2 59x10 3 F

Write the Babylonian numeral as a Hindu A WWW Hindu Arabic numeral is 329 Hindu Arabic

Write the Babylonian numeral as a Hindu Arabic numeral WWVY uivalent Hindu Arabic numeral is Baby Hindu Arabic

Write the Babylonian numeral as a Hindu Arabic numeral 1 F

Listen Determine lim ex 2 x48 O 0 O 8 01 2 01 8

Determine the integral f edx O2e1 O 2e c O2e c X Oe c

Multiply in the indicated base 6AB12 8912 X X 6AB12 8912

ert the numeral to a numeral in base 10 53616 53616 10

ultiply in the indicated base 248 x318 248 318

Convert the numeral to a numeral in base 10 60512 60512 10

Subtract in the indicated base 11012 1102 1 11012

Suppose a base 4 numeration system has its digits represented as sh Write the Hindu Arabic numeral equivalent to RB4 The value of ORB 4 in base 10 is Simplify your answer COO R 1 0 2 G 3

Suppose the symbols to the right represent numerals in a base 4 numeration system Write the Hindu Arabic numeral equivalent to the following 00 00 1 Simplify your answer B R 1 G

Subtract in the indicated base 77309 21769 77309 21769

Listen Determine f x for f x 4x 5e x e f x 10x xe e 8e x Of x x xe e 10e f x 8x 2e 10e x f x 8x xe 10e Of x 8x xe e 10e

Write the Babylonian numeral as a Hindu Arabic num 1 The Hindu Arabic numeral is 683

y 36 3x List the intercepts Select the correct choice below and if necessary fill in the answer box within your choic OA The intercept s is are Simplify your answer Type an ordered pair Use a comma to separate answers as needed OB There are no intercepts Test for symmetry Select all that apply A The graph is symmetric with respect to the origin B The graph is symmetric with respect to the y axis C The graph is symmetric with respect to the x axis P The graph is not symmetric with respect to the x axis y axis or the origin

Height of a Rocket A toy rocket is shot from a platform 21 feet above the ground The rocket flies into the air reaches a maximum height of 48 feet then falls to the ground The graph of H t below shows the height of this rocket in feet t seconds after launch Approximate the average rates of change over each of the following time intervals Round to two decimal places 0 seconds to 30 seconds feet per second 30 seconds to 70 seconds feet per second 0 seconds to 70 seconds feet per second V o Height of Rocket feet 50 30 20 20 5 5 10 15 20 25 30 35 40 45 50 55 60 65 70 Time seconds

Find the average rate of change for the scenario provided exact decimal or reduced fraction and choose the appropriate units Miles 400 360 320 280 240 200 160 120 80 40 Units Avg rate of change O 2 O 4 6 hr day mi 8 10 12 14 16 18 20 Gallons day ft 8 hr O 8 ft day gal mi

Write the Babylonian numeral as a Hindu Arabic numeral 1 T The Hindu Arabic numeral is 33 060

Convert the base ten numeral to a numeral in base four 110

represents the cost C of using m anytime cell phone minutes in a month for a five person family plan C Cost dollars 2000 1000 0 108 0 3000 360 1000 100 13800 1764 5000 10000 m Number of minutes 15000 c Determine C 3000 Interpret this value C 3000 360 Now interpret the value of C 3000 Choose the correct interpretation below A The value of C 3000 represents the monthly charge if 3000 minutes are used B The value of C 3000 represents the monthly charge if each person on the plan uses 3000 minutes OC The value of C 3000 represents the minutes used that correspond to a monthly charge of 3000

Convert the numeral to a numeral in base 10 324 324 10

Convert the numeral to a numeral in base 10 113 113 10

Write the Mayan numeral as a Hindu Arabic numeral 0 21 10 11 12 3 www 13 4 14 5 1 15 E 16 eral is 7 17 8 18 9 19

Find the following for the function f x x 3 a f 0 e f x b f 6 1 f x 6 c f 6 g f 7x a f 0 Simplify your answer Type an integer or a fraction www d f x h f x h

D D Write the given numeral as numerals in the Hindu Arabic Roman traditional Chinese and Greek systems of numeration 999 O A Choose the correct equivalent Greek numeral below OA f B ate OC p OD yo OB 1 O C HI SO D

Write the given numeral as numerals in the Hindu Arabic Roman traditional Chinese and Greek systems of numeration 99999 What is the equivalent Hindu Arabic numeral Type an integer What is the equivalent Roman numeral Choose the correct equivalent Chinese numeral below OA Ho B K OC K O D

A 25 foot ladder is leaning against a house as shown in the figure below 2x 625 x 25 ft When the base of the ladder is pulled away from the house at a rate of 2 feet per second the top will move down the wall at a rate given by the following equation where x is the distance between the base of the la and the house and r is the rate in feet per second 2 ft sec X ft sec a Find the rate r in ft sec when x is 7 feet 7 12 ft sec b Find the limit of r as x approaches 25 from the left 0

f x 8x 5 and g x 8x 1 For each function h given below find a formula for h x and the domain of h Enter the domains using interval notation A h x fog x h x Domain B h x gof x h x Domain C h x ff x h x Domain D h x gog x h x Domain

be able to come back to the skipped part Tutorial Exercise Find the limit if it exists lim f x where f x X 6 x 3x 4 if x 6 x 3x 40 if x 6 Step 1 Find the value of the function as x 6 That is the limit from the left Thus lim f x lim X 6 X 6 X means that x approaches 6 from values less than 6

points Q What did one calculus book say to the other A Don t bother me I ve got my own problems 7 10 pts Prove using the mathematical definition lim X 3 X 3 X

What did one calculus book say to the other A Don t bother me I ve got my own problems 10 pts Mathematically determine if f x sin x tan x tinuity What is the lim f x x 1 is continuous at x 1 by using the three criteria for

Q What did one calculus book say to the other A Don t bother me I ve got my own proble 4 5 pts Prove using the mathematical definition lim 2 0 2x 5

Find the real solutions of the equation Verify your results using a graphing utility y 3 7 Select the correct choice below and if necessary fill in the answer box to complete your choice OA The solution set is Simplify your answer Use a comma to separate answers as needed al solutione

Solve the equation 3 3 2x 5 x 5 Select the correct choice below and fill in any answer boxes in your choice OA The solution set is Simplify your answer

Write the number as a Babylonian numeral 242 Choose the correct answer below OA TTTT TT OB T7777777 OC TTTTT O D TTT TT

State two other ways to name Zx Two other ways to name Zx are Use a comma to separate answers as needed X n B

The perimeter of a rectangle is 84 feet Find its dimensions assuming that its length is 3 feet less than twice its width The width is and length is Simplify your answers

is structured so that you will read some information and maybe watch a video ote You may repeat this tutorial as many times as you like What is lim d t t

What is the reference angle of 609 The reference angle of 609 is

Find the midpoint of the line segment joining the points P and P P 2 4 P 4 6 The midpoint of the line segment joining the points P and P is Simplify your answer Type an ordered pair

Determine which of the given points are on the graph of the equation Equation y x x Points 1 1 0 0 1 2 Which of these points are on the graph of the equation Select all that apply A 1 1 B 1 2 C 0 0

Listen Choose an equation from the following that expresses the fact that a function f is continuous at the number 6 Olim f x x 6 10 Olim a 1 0 f x 0 lim fx x 6 f x sease w m6

Listen Determine where f is discontinuous x if x 0 5 x if 0 x 5 5 x if x 5 2 fx O0 only O5 only O and 5

Determine the limit lim 1 x 1 x 1 01 O 1 0 O 0