Limits & Continuity Questions and Answers

graph of a function y f x is shown below Use it to answer the questions Enter DNE a value does not exist enter o if the limit approaches positive infinity or o if the limit approaches negative infinity 5 4 3 2 YA 4 fuff 1 2 3 4 5 6 3 2 It is continuous at this point 1 1 2 What is a reasonable estimate for lim f x x 2 What is a reasonable estimate for f 2 What is the best description of the function at x 2 Select an answer There is an infinite discontinuity at this point There is a removable discontinuity at this point f x f x x ion at x 0 X

The graph of a function y g x is shown below Use it to answer the questions 7 6 5 3 2 Y 7 6 5 4 34 2 14 2 3 5 6 123 B 56 HA What is a reasonable estimate for lim g x What is a reasonable estimate for lim g x What is a reasonable estimate for g 2 What is the best description of the function at x 2 O There is a removable discontinuity at x 2 There is a jump discontinuity at x 2 There is an infinite discontinuity at x 2 It is continuous at x 2

Let f x mx 14 m x 9x 5 if x 9 if x 9 If f x is a function which is continuous everywhere then we must ha

5x 14 Let f x x 82 2 if x 1 if x 1 if x 1 Select all statements below that you agree with Note You may be checking more than one box No partial credit O f 1 is defined Olim f x exists x 1 Olim f x f 1 x 1 The function is continuous at x 1 The function is not continuous at x 1

The graph below is the function f x 5 4 3 2 1 32 3 2 3 1 2 3 4 s q Select all statements below that you agree with Note You may be checking more than one box No partial credit Of 2 is defined Olim f x exists x 2 Olim f x f 2 x 2 The function is continuous at x 2 The function is not continuous at x 2

Determine the domain and range of the function V 4 3 2 1 4 3 2 1 1 2 3 4 y 1 2 3 4 x

Find the exact value of each expression Enter your answer in radians a in 1 b cos 1 13

Find the absolute maximum value of the function f x x e maximum value

Find the limit cos x lim e 3x x 00

Question Given f x 2x 10x 12 OC 7 Select the correct answer below which of the following statements are t Of x has a removable discontinuity at a 7 Of x has a jump discontinuity at x 7 Of x has an infinite discontinuity at a 7 Of x is continuous at x 7

7 f x int x or f x x Find A f 2 9 C f 3 1 B f 3 8 D f 2 3

Part 1 of 3 O Points A car dealership has 8 red 9 silver and 4 black cars on the lot Ten cars are ran of the dealership Complete parts a through c below a Find the probability that 4 cars are red and the rest are silver Round to four decimal places as needed

Question 14 8 5 37 LS he table shows relative frequencies for red green color indness in one doctor s practice M represents person is ale and C represents person is color blind Use this ble to find the probability P M n C MnC HW Score 50 10 of O Points 0 of 1 M M 0 032 0 00 C 0 477 0 48 Totals 0 509 0 49 C

0 6 6 14 a Plot O S the points in a coordinate plane No Solution Help 2 1 20 19 18 17 16 542 22 15 14 13 12 11 10 9 8 7 5 4 3 2 1 1 2 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 Clear A Fill WebAssign Graphing Tool

Simplify the expression Assume that a denotes a positive number 16a a

many different committees can be formed from 7 hers and 45 students if the committee consists of 4 hers and 4 students In how many ways members be selec

Part 1 of 2 O Points 0 of 1 ain country s postal service currently uses 5 digit zip codes in most areas How many z are no restrictions on the digits used How many would be possible if the first number many zip codes are possible if there are no restrictions on the digits used

Let lim f x 9 and lim g x 7 Use the limit rules to find the following limit X 4 X 4 lim X 4 f x g x 2g x f x g x 2g x lim X 4 Type an integer or a simplified fraction

10 98 8 5 4 3 lim f x 6 lim f x I 6 lim f x I 46 lim f x 2 5 lim f x 2 5 lim f x I 5 Use the graph f x above to determine values for the following Enter DNE if the value does not exist f 6 4 2 6 4 f 5 3 2 2 3 6 7 9 X X X X X X 6 X 10 X

Let f z 1 2x 14 if z 6 Calculate the following limits Enter DNE if the limit does not exist lim f z lim f z 5 2 1 if z 6 if z 6 lim f z

Enter a whole or decimal number or DNE for does not exist or undefined 10 x x 0 lim 5 110

2 x r if x 3 2x 7 if x 3 Calculate the following limits Enter DNE if the l mit does not exist Let f x lim f x 2 3 lim f x I 3 lim f x 2 3

2 7x 7x 5 8 sin x Find the following limits lim f x 0 x 0 Let f x lim f x x 0 lim f x x 0 if x 0 if x 0 help numbers help numbers help numbers

Evaluate the limit Y 6 lim y6 y 6

Evaluate the limit lim x 4 x x 12 x 4

Evaluate the limit t 27 lim t 3 t 3

The limit represents lim h 0 a derivative f a Find f and a sin h 3 h Express numbers in exact form Use symbolic notation and fractions where needed f x a

Find all values of c such that the limit exists lim x 1 x 8x c x 1 Give your answer in the form of a comma separated list Express numbers in exact form Use symbolic notation and fraction where needed Enter DNE if there are no values of c such that the limit exists

Find the horizontal asymptotes of g 8 1 10 11 4 Give your answer as a comma separated list of equations Express numbers in exact form Use symbolic notation and fractio where needed Let y f x and give the equations in terms of y and x horizontal asymptote s

Find the horizontal asymptotes of f x 3x 6x 9 4x 6x4 Use symbolic notation and fractions where needed If there are more than one horizontal asymptote give them as a comm separated list Equation s

8 Make a careful sketch of the graph of f x sinz on the axes below On the same axes sketch the graph of its derivative Can you guess what the derivative of the sine functions is from its graph 2 T 3 r 2 T 2 y 1 2 0 1 2 TC 3r 2 2T

given matrix is invertible find its inverse A 6 0 0 20 08 Select the correct choice below and if necessary fill in the answer box to complete your choi On OA A Simplify your answers The motrix is not invertible

Let g x Evaluate the following lim q x I b lim g x x b a x b 146 c x b a x b c x b C q b C lim g x c x b help numbers

Let f x 9x X 0 Evaluate the following lim f x I 0 lim f x x 0 f 0 lim f x I 0 if x 0 if x 0 help numbers

Order these numbers from least to greatest 2 17 2 2 2 017 2 1761 2 17 2 2 2 017 2 17

A graphing calculator is recommended For the limit lim x 2 x3 5x 4 2 illustrate this definition by finding the largest possible values of that correspond to 0 2 and 0 1 Round your answers to four decimal places

A certain state uses the following progressive tax rate for calculating individual income tax Income Range Progressive Tax Rate 2 5 9001 and up 5 4 Calculate the state income tax owed on a 30 000 per year salary tax 0 2000 2001 9000

For handwritten assignments you need to show all work and all the steps wherever necessary If you just write down the final answer without showing any work you will get only partial credit Exercise 1 Let f x 2 cos 2r 1 1 Find the domain and the range of f 2 Sketch the graph of f using the transformation rules in Section 1 3 and mark the x intercepts and y intercepts on the graph Recall that the x intercepts of a graph are the x coordinates of the points where the graph intersects the r axis They are found by setting y 0 in the equation of the graph Similarly the y intercepts of a graph are the y coordinates of the points where the graph intersects the y axis They are found by setting x 0 in the equation of the graph

The expression In z 6 ln t In 9 can be simplified to In w where w

Find the exact value of each function for the given angle for f 0 sin e and g 0 cos 0 Do not use a calculator 0 2 3 a 0 5 f g 0 b g f 0 0 5 c g 0 0 25 d fg 0 0 e f 20 0 f g 8 X X X

For what values of x does f x 5x 10 sin x have a horizontal tangent line Choose the correct answer below TU 5 O A x 2k and x 2k where k is any integer 3 3 T 5ft B x 2kx and x 2kx where k is any integer 6 T 5T O c x k and x k where k is any integer 3 3 R6 OD x k and x 5T 6 k where k is any integer

9 The speed of a runner increased steadily during the first three seconds of a race Her speed at half second intervals is given in the table Find lower and upper estimates for the distance that she traveled during these three seconds 0 0 5 1 0 1 5 5 2 0 2 5 3 0 10 8 14 9 18 1 19 4 20 2 t s v ft s 06 2

A Sketch the graph of the following f x left begin array c 1 function text if x 5 3 text otherwise B For the end array right function above what is lim f x x 3

Find an equation of the line L An equation of the line L is Simplify your answer Lico intogoro

y 2 c Let f y left begin array ll text if y in infty 8 c y 9 text if y in 8 infty end array right For what value of the constant is the function C f continuous on and 0 0 C Hint Compute lim f y y 8 lim f y y 8

Consider the following functions f x 8x7 g x Find f o g x Find the domain of fog x Enter your answer using interval notation Find g o f x Find the domain of gof x Enter your answer using interval notation Find f o f x Find the domain of f o f x Enter your answer using interval notation Find g o g x Find the domain of go g x Enter your answer using interval notation

Find the rate of change where x xo y x2 5X XO 6 O 17 O 1 11 7 dx

Find the indicated one sided limit If the limiting value is infinite indicate whether it is or 0 lim 5 f x and lim x 5 f x where f x lim x 5 f x 15 f x 0 lim lim x 5 f x 00 x 5 f x 15 lim x 5 f x lim lim 10 x 5 f x 15 lim x 5 f x 15 lim x 5 f x 1 10 if x 5 5 x 2x if x2 5

lim Find f x if it exists x a h 00 O a b The limit fails to exist

The graph of y f x is shown Use the graph to answer the questio Find 4 lim x 1 f x and O 2 7 O 7 2 10 O 7 7 lim x 1 f x does not exist does not exist