Limits & Continuity Questions and Answers

Consider the following graph of two functions Step 1 of 4 Find f g 1 7 Ay f N Enable Zoom Pan RA

Step 3 of 4 Find fg 1 17 y f Enable Zoom Pan 2

Step 2 of 3 Use the following information to find 8 f x Answer 2 Points gof x 10 f x 4x 2 5 and g x 3x 2 2

3 Determine whether the sequence converges or diverges If it converges give the limit a 1 4 9 16 n 1111 2 4 8 16 b 3n c 30 1 2 3n 1 2

Suppose the scores of students on an exam are Normally distributed with a mean of 333 and a standard deviation of 67 Then approximately 99 7 of the exam scores lie between the numbers and such that the mean is halfway between these two integers You are not to use Rcmdr for this question

28 3 2 4 7 5 A log 3 2 log 2 4 7 log 5 Express log B log 3 2 log 4 7 log 5 as an algebraic sum of logarithms C log 3 2 log 4 7 log 5 1 1 D log 3 2 log 4 7 log 5

14 x log3 200 An intermediate step is log10 200 log 0 3 A B log 0 3 log 0 200 C log103 200 D 200 log10 3

19 Perform the indicated operation leave the answers in the rectangular form a bi 2 3i 2 3i A 5 12i 13 B 1 C D 5 12i 13 5 12i 5

You pick a card at random put it back and then pick another card at random 6789 What is the probability of picking a divisor of 18 and then picking a number greater than 8 Write your answer as a decimal

10 Perform the indicated operation leave the answers in the rectangular form a bi Simplify 6 8 2 4 5 18 A 20 2 4i B 201 2 4i C 27i 2 4i D 27 2 4i

7 Use logarithms to evaluate 7 512 What is the answer A 2 741 B 9 994 C 1 830 D 5 438

You spin the spinner once 6 7 5 8 4 23 What is P greater than 2 or factor of 90

Complete the congruence statement 3 38 in L 28 ALKJA 43 in 20 in 62 K T 20 in 62 S 43 in 38 in 28

7 Show that an neN CR is bounded if and only if lim supn an 00 8 In this question you may not use the fact that Cauchy sequences are equivaler

and the eighth term of the recursively defined sequenc 3 and d 1 5 for 22 11

Look at this diagram R d Q M If LN and OQ are parallel lines and mZOPR 41 what is m O

Find EF in parallelogram EFGH 5W 92 F E G W H

Find the measures of the angles labeled in the figure on the right mZEFD m EHF m HFG m G mZE O O O O O E do Co H 500 330 bo 20

Use the frequency distribution to complete parts a through e a Determine the total number of observations b Determine the width of each class c Determine the midpoint of the second class d Determine the modal class or classes e Determine the class limits of the next class if an additional class were to be added a The total number of observations is 27 b The width of each class is 8 c The midpoint of the second class is 21 5 Type an integer or a decimal Class 10 17 18 25 26 33 34 41 42 49 50 57 Frequency 152847 d The modal class es is are 34 41 Use a hyphen to separate the limits of a class Use a comma to separate answers Type the classes in order from smallest to largest

as Express 163 1 2 15 Single kgarithm

A company manufactures microchips The Revenue function is given by R x 75x 3x and the Cost function is given by C x 125 16x where x is millions of chips produced and R and C are millions of dollars 1 x 25 How many million chips should be produced to maximize Revenue B What are the fixed costs C Find the Profit function 5 400 200 200 400 600 800 5 10 15 20 29 x from 5 to 75x 3x E Find the two values where Profit 0 16x 125 D What is the average cost for producing 6 million microchips

etermine whether the series is convergent or divergent If it is convergent find its sum If the quantity diverges enter DIVERGES DIVERGES cos 5

Use the linear approximation of the function f approximate the number 9 08 3 2556 3 4445 3 4556 3 1556 3 0133 9 x at a 0 to

8 pts Series Solutions Find and classify the singular points of the equation x 1 x 2 y 2x y 4y 0

Problem 1 Find the amplitude period frequency and phase shift of the function whose graph is given below if the point a f a is and the point b f b is UI a f a b f b If we call the period P what is the distance a and b in terms of P If we call the amplitude A what is the distance between f a and f b in terms of A

1 Show that if f VR is such that all its sublevel sets are convex sets then f must be quasiconvex Here as usual V is a real normed vector space

3 Solve on a calculator but show work sec 8

The graph of f is shown What is the value of f x dx 2 1 ol 1 2 2 2 2 3 4 2 4 6 7 2 7 x 0

You pick a card at random 1 2 3 4 5 What is P 2 or prime Write your answer as a percentage

MUN GAGA endaon What is P heads or tails

Evaluate the following limit lim O 7Inx lim x 19x 9 7 x 19x 9 27 7lnx Olim 3 7Inx x 19x 9 Olim lim 0 7Inx 7 27 7Inx x19x 9 7

Evaluate the following limit lim x sin 8x X 0 O lim x sin 8x 0 vint O lim x sin 8x 8 vint Olim x sin 8x 1 vint O lim x sin 8x 8

Evaluate lim O 8 O 7x 1 x 2 x 2 O Does not exist 00 by graphing

Evaluate lim O 5 0 00 O 0 5x 13 X 3 by graphing

Suppose 2x 15 f x x 4x 3 for all x values near 6 except possibly at 6 Evaluate lim f x X 6 O lim f x does not exist O lim f x 12 Olim f x 3 V15 Olim f x 3

For 0 find 0 necessary to prove lim 9x 30 15 X 5 0 0 O 40 0 6 5 5

Evaluate lim substitution O O O O lim 2x 9x 9 x 34x 9x 9 x 34x 9x 9 2x 9x 9 1 5 2x 9x 9 lim x 3 4x 9x 9 lim 2x 9x 9 x 34x 9x 9 lim 2x 9x 9 x 34x 9x 9 does not exist 1 algebraically by simplifying if possible then using direct 1 2

Use a table of values to evaluate lim X 0 Olim X 0 Olim X O sin 5x X Olim X 0 lim sin 5x X sin 5x 5 sin 5x 5 X Y does not exist 0 08727 sin 5x X

Find f g 3 for the following functions f x x and g x 5x 11

en f x find g x and h x such that f x g h x and neither g x nor h x is solely x f x x 2 1 er g x

For the function y p x graphed below determine the signs positive negative zero for the values on the right 6 2 6 0 4 A p 2 B p 2 C p 2 D p 2 E p 2 F Find one x value where p x 0 and p x

Given f x find g x and h x such that f x g h x and neither g x nor f x is solely r f x 2x 1 3 swer g x

g 2 for the following functions er your answer opens in new window f x x 1 and g x 2x 5

nd f g 1 for the following functions Round your answer to two decimal places if necessary er f x x 4 and g x 16x 9

lim an 318 Need Help Read It 0 1 Points DETAILS Watch It SCALCET9 11 XP 1 018 Determine whether the sequence converges or diverges If it converges find the limit If an answer does not exist enter DNE en e n e2n 2

Consider the following functions f x x 4 and g x Step 2 of 2 Find the formula for gof x and simplify your answer Then find the domain for gof x Round your answer to two decimal places if necessary Answer gof x x 1 2 3 Key Keyboard Sho

Consider the following functions f x x 4 and g x Answer Step 1 of 2 Find the formula for fog x and simplify your answer Then find the domain for fog x Round your answer to twa decimal places if necessary x 1 2 fog x In K Keyboard S

lim an 818 an Need Help n 3 4n 3 Read It 1 Points DETAILS SCALCET9 11 1 041 Determine whether the sequence converges or diverges If it converges find the limit If the sequence diverges enter DIVERGES 1 8 n

lim 318 nan an Need Help 1 Points 3 7n n 5n Read It DETAILS Watch It Master It SCALCET9 11 1 035 Determine whether the sequence converges or diverges If it converges find the limit If the sequence diverges enter DIVERGES an e 3 n

Question 1 of 12 Step 2 of 2 Consider the following functions Step 2 of 2 Find the formula for decimal places if necessary Answer 1 18 Correct f x 2x and g x x 3 x and simplify your answer Then find the domain for 2 a x Round your answer to two Key Keyboard Sho