Limits & Continuity Questions and Answers

Find the following using the table below 1 2 3 4 3 1 4 1 2 4 3 2 1 4 1 3 2 4 X f x 2 f x 3 g x g x if h x f g x then h 3

Sketch a graph of a function that satisfies all of the given conditions lim x 00 lim x 00 lim x 0 lim x 00 x18 x11 x 0 O y x 1 JAA lim x 00 X 0 x 1 x 1

Identify the function whose graph is shown below ZTT O y sin 2x 1 AN TT 1 O y sin x 3 O y cos x 2 2 Y 3 ZTT X

20 B OXER Ox 3 X 3 X ER 10 X 3 X x R X 3 X ER y f x 10 The domain of the function f x would be 20

Let f x 4x 28 if x 6 if x 6 if x 6 x 22 2 Select all statements below that you agree with Note You may be checking more than one box No partial credit Olim Of 6 is defined lim I 6 f x exists f x f 6 I 6 The function is continuous at x 6 The function is not continuous at x 6 Question Help Message instructor

Sinx 7x Sin X emm lim 2 No Sin 0 3 vertical asymptote X 0

olve for x x 1 2 x 3 x 4 O x 5 X 6

Evaluate the limit lim x 0 3x 25 5 fraction X A Make sure your answer is a decimal and not a

lim J X 0 Sin X vertical asymptote X 0 x 0

Find all solutions to 2 cos 0 3 on the interval 0 0 2 0 Give your answers as exact values as a list separated by commas Question Help Video 1 Video 2 Message instructor

The period of y cos4x is TT 2 O 2 T

Example Determine whether the series converges If it converges give the sum k 16 0 25 k 1 100 ris 00 n 0 72 0 1 0 01 0 001

Question 7 Find the limit lim I 64 x 8 X 64 Give an exact answer or keep at least three d Question Help video Message instructor

10 a lim ex cos 2x X 0 b lim 4 sin x x 0 tan x

9 lim X 5 4416 13 Sin 24 2 tan 5x 3 Sin 2 510 2 tan 5 STC

13 find lim f x X 2 3 where f x x x 1 4x 6 4x 3 if x 2 if x 2

2 lim t t sinx 2 in 0 sin 0 18

Evaluate the trigonometric function sin 4

Let f x 2x 3x 5 and g x x 14 Find the limits lim g f x x 1

2 f x X 1 x 3x 4 lim X 14 X 1 x X 4 V A X 1 and 4

Find the values of the six trigonometric functions of 0 where is the angle shown in the right triangle in the accompanying figure sin 0 cos 0 tan 0 csc 0 sec 0 cot 0 A 13 0 5 C BO

Question 15 Let h v 137 log13 v Determine the derivative of h dh dv

Find all values of such that is continue on son f x 1 x x5c

Given that lim f x 6 and lim g x 7 find the following limit X 1 X 1 lim 8f x g x X 1 lim 8f x g x X 1 Simplify your answer

et f x x 121 x 11 121 x 11 if x 0 if x 0 lim f x b lim f x and c lim f x X 11 X 0 X 11 Find a lim

lim 4x40 x Ax 15 x Ax 10 x 15x 10 Ax

Sketch a graph of the function f x 2 2 5 sin 4x 4 3 2 1 7 8 3 4 5 8 T 2 3 8 4 8 1 2 3 7 8 4 3 8 T 2 5 8 3 4 7 8

Let 11 12 Part A Determine tan 8 using the sum formula Show all necessary work in the calculation 5 points Part B Determine cos using the difference formula Show all necessary work in the calculation 5 points

4 The final examination results obtained by a group of 3200 Biology students are summarized on the cumulative frequency graph cumulative frequency 3500 3000 2500 2000 1500 1000 500 0 0 20 40 Examination result x Frequency 60 examination results 0 x 20 80 150 100 4a Find the median of the examination results 2 marks 3 marks 4b Find the interquartile range 4c The grouped frequency table below summarizes the examination results of this group 2 marks of students Write down the modal class 1100 40 x 60 20 x 40 350 x 4d Write down the mid interval value of the modal class loto an estimate of the mean examination result 60 x 80 1400 80 x 100 ctions Th e followin 200 tC 1 mark 2 marks

To find the distance across a small lake a surveyor has taken the measurements shown Find the distance across the lake using this information C distance 2 29 km 48 9 NOTE The triangle is NOT drawn to scale 3 65 km km B A O

Problem 9 Expand the logarithmic expression log b b c 1 Show your work

1 For y 6 cos X its amplitude is its period is

The graph below is the function f x 54 24 2 Find lim 54 4 3 2 Find lim 24 1 03 Find lim 1 1 2 3 4 f x f x f x Find f 1

The graph below is the function f x 5 4 3 2 1 3 2 1 Olim 1 12 2 3 2 2 34 Select all statements below that you agree with Note You may be checking more than one box No partial credit 2 3 4 5 Of 2 is defined Olim x 2 f x exists f x f 2 The function is continuous at x 2 The function is not continuous at x 2

Indicate whether the graph specifies a function Q 51 Ay 10 15 15 10 15 X 10 G The graph does not specify a function O The graph does specify a function

Find lim h 0 f 7 h f 7 h f 7 h f 7 lim h h 0 if f x 6x 11 Simplify your answer

Find lim h 0 d lim h 0 f 5 h f 5 h f 5 h f 5 h if f x x 9 Simplify your answer

Find b without a calculator log 664 3 b

Write the given set in interval notation and graph the set on a number line x 1 x 5 Use interval notation to express the set What is the resulting interval Graph the set on a number line Choose the correct graph below OA O C 9 G 10 10 OB OD

Find the limit if it exists lim 11x 6 X 4 Which of the following shows the correct expression after the li O A lim 6 X 4 OB 11 lim x lim 6 X 4 X 4 O C 11 lim x lim 6 X 4 X 4 OD 11 lim x

Use the graph of y g x to graph the given function O y g x 44

Evaluate lim xax x A B 0 C 1 D 0 X 00

The data in the table gives some of the properties of the star Mu Cephei Apparent magnitude 4 23 Absolute magnitude 6 81 Surface temperature 3227 C i Calculate the wavelength of the peak in the black body radiation curve for Mu Cephei ii Copy the axes below and sketch the black body radiation curve for Mu Cephei Label the wavelength axis with a suitable scale

Refer to the graph of y f x to the right to describe the behavior at the limit lim f x Use and X 2 where appropriate Select the correct choice below and fill in any answer boxes in your choice O A lim f x X 2 B The limit does not exist and is neither nor Ay 10 G

Find the limits in a through c below for the function f x X 9x 8 X 8 O A lim f x x 8 Simplify your answer Use and when appropriate OB The limit does not exist and is neither nor o c Select the correct choice below and fill in any answer boxes in your choice ALE

Use the 8 definition of limit to show that lim z 1 i 2z 3i 2 5i

Differentiate h 0 h 0 0 sin 0 0 cos 0 20 sin 0

If f x f 4 x 2 x Ent find f 4 X

Question 19 If f 14 f 0 3 and f x 2 for a 14 0 what is the smallest value f 0 can possibly be Submit Question

The graph of f x is given below Find the domain and range of f x Domain 2 10 Range 4 4 Domain 2 x Range 4 Domain 2 Range 4 Domain 2 x Range 10