Questions

sin 2x Which of the following is equal to sin 3x 2x 3x 2x sin 2x 2x sin 3x 3x sin 2x 3x sin 3x 2 sin x 3 sin x assume0 Select all that apply

Which of the following graphs exhibit ALL of the listed properties lim f x 2 818 lim f t o 2 f 2 is undefined 54 3 2 1 54 3 2 1 54 3 2 1 4 3 2 4 S 4 3 2 1 2 4 S 5 4 3 2 1 1 2 3 5 3 2 P DE 1 1 2 34 5 2 a 3 4 2 B q 70

Which of the following graphs exhibit ALL of the listed proper lim f x 2 HIX lim f x 00 I 1 f 1 2 54 3 2 1 51 4 13 2 1 1 2 3 4 54 5 54 3 2 1 4 3 2 1 2 3 4 st 3 2 54 3 2 1 2 1 2 3 1 2 3 4 5 La 4 5 1 2 3 4 a

The graph below is the function f x 8 7 16 15 lim f x 8118 2 1 8 7 6 5 4 3 2 1 2 3 34 4 5 56400 6 7 8 1 2 3 4 5 6 7 8

The graphs of y f x solid and y g x dashed are shown The two curves intersect at 5 0 Determine the sign of the following limits You may assume the limits exist lim f x g x is 5 Positive Negative Zero lim f x g x is 20 Positive Negative Zoro

olve the absolute value inequality Graph the solution set and write the solution in interval notation a b 4 5 114 25 3 IT 7 114 25 6 25 2 25 6 25 6 25

Find the value s of k such that f x is continuous everywhere Sx 76 a 2 4x3 3kx 2 x 2 q f x

The graph of y f x has the following features f 1 0 lim f x 2 x 1 lim f x 1 1 Which of the following might be a graph of y f x a Q a

Solve the inequality Write the answer in interval notation 4x24 and 14 x 7 a 7 00 b 1 7 c 0 00 d 1 7 a Ob c O d

12 If the function f is continuous for all real numbers and if when x 3 then f 3 f x x 6x 9 x 3

If two pyramids are similar and the ratio between the lengths of their edges is 4 9 what is the ratio of their volumes O A 16 81 O B 81 16 O C 4 9 D 64 729

x 3x 7 x 3 3 x 1 x 1 8 g x 2x 1 In x a at x 3 ran b at x

Solve for the indicated variable C 27r for r 2C a r a C 2T Ob b r T d Oc c r 2 C T 20 d r

because there the most sensitive Explain your answer Hearing is the most senso a lot of ways to hurt your hearing are 2 Identify one or more ways that each of your senses helps you move through and experience the world around you

stion 1 Sickle cell anemia is a genetic disease resulting from a copying error for the DNA sequence that codes for Beta hemoglobin the molecule that assists red blood cells with transporting oxygen The mutated mRNA sequence has the nucleotide uracil instead of adenine in the seventh codon as illustrated in the sequence below Apply your knowledge of transcription translation and mutations to answer the following questions a Is sickle cell anemia created by a point or frameshift mutation b What are the coding and template strands of DNA that correspond to the provided mRNA sequence 5 AUG GUG CAC CUG ACU CCU GUG GAG AAG 3 B 1 EE T U T T 0 Word s

If the ratio between the radii of the two spheres is 3 7 what is the ratio of their volumes OA 27 343 OB 21 49 C 9 49 7 3

falfio anubic Human Hom Sapiens Domestic cat Felis Catus Striped hyena dag canis Lupus Mans Mas Musculus Brown rat Rattus norvegicus Gerbil Mexiones unguiculatus

Let f x x a Simplify f 13 h f 13 h Algebraically simplify your answer until you have cancelled out the factor of h in the denominator Hint See Problem 9 on Assignment 2 2 for similar computations 1 13 h 13 b Evaluate lim f 13 h f 13 h 0 h If an answer does not exist enter DNE dne X c Determine the equation of the line tangent to y f x at x 13 y 1307

Suppose a vat contains 15 liters of water and 12 kg of salt At t 0 water is added at a rate of 20 liters minute while salt is added at a rate of 9 kg minute A function giving the concentration after t minutes will be C t express as a function of t As time passes the concentration will Decrease Increase to kg liter kg liter

The graph of y f x is shown below b Is f x continuous at x 0 OYes No From left to right the graph starts below the x axis for negative values of x and decreases to negative infinity as x approaches zero from the left There is no point on the curve when x equals zero Then for positive values of x the graph decreases from positive infinity and approaches the x axis from above Answer each of the following questions about f x You have one submission for each question a Does lim f x exist x 0 OYes No c Is f x differentiable at x 0 Yes No 2

The two solids are similar and the ratio between the lengths of their edges is 2 9 What is the ratio of their surface areas O A 8 36 B 4 18 C 4 81 161 18 36 8

The two solids below are similar and the ratio between the lengths of their edges is 4 5 What is the ratio of their surface areas OA 16 25 B 16 20 OC 64 125 01 5 4

The graph of y f x is shown below 1 b Is f x continuous at x 1 OYes No Answer each of the following questions about f x You have one submission for each question a Does lim f x exist x 1 OYes No c Is f x differentiable at x 1 Yes No d Does lim f x exist X 2 OYes No The graph of a parabola that opens up with a hollow point on the graph when x 2 e Is f x continuous at x 2 OYes No f Is f x differentiable at x 2 2

The graph of y f x is shown below 3 X 2 Answer each of the following questions about f x You have one submission for each question a Does lim f x exist X 3 Yes ONO b Is f x continuous at x 3 Yes No c Is f x differentiable at x 3 Yes No d Does lim f x exist X 1 CYes No e Is f x continuous at x 1 Yes No 2 f Is f x differentiable at x 1

Find the limit sin 5x 3x lim x 0 3x 40 sin 5x lim

If two cylinders are similar and the ratio between the lengths of their edges is 4 3 what is the ratio of their volumes A 16 9 B 4 3 C 64 27 D 16 27

Use the Y screen to write the equation being solved Then use the table to solv Plot1 Plot2 Plot3 X Y Yt 2 X 3 Y2 2 3 2X Y3 AY4 Y5 Y6 Y7 O C 2 X 3 2 3 2X 2 O D 2 X 3 0 and 2 3 2X 0 OE 2 X 3 2 3 2X 3 OF 2 X 3 2 3 2X 0 O G 2 X 3 2 3 2X 3 2 1 3 X 3 12 10 8 6 4 110 Y 2 Part 1 of 2 18 14 10 840 6 2 6

The graph below is the function f x 8 7 6 5 4 3 2 lim f x 2 8 8 7 6 5 4 3 27 1 2 AWN 3 4 567 7 8 4 5 6 7 Enter the limit If the limit is o enter oo If the limit is enter oo If no limit exists enter

Suppose f x has the following values I f x lim 8 7 9 7 99 6 5 6 05 1 6 f T 7 999 8 6 005 9 appears to be 8 001 6 004 8 01 6 04 8 6

Determine whether each statement is true or false You have one submission for each statement a For every function f x if f x is continuous at x a then f x is also differentiable at x a True False b For every function f x if f x is differentiable at x a then f x is also continuous at x a True False

The graph of y f x is shown below b Does lim f x exist x 1 CYes No c Doesf Answer each of the following questions about f x You have one submission for each question a Does lim f x exist x 1 Yes No fix exist Yes No From left to right the graph is a horizontal line to a hollow point at 1 1 Then the graph jumps to a filled in point at 1 3 and continues to the right as a horizontal line c is fix continuous at x 1 CYes No 1 e Is x differentiable at x 1 CYND 2 3

The graph of y f x is shown below 3 2 b Is f x continuous at x 3 OYes No d Does lim f x exist X 1 OYes No The graph of the function decreases linearly with a slope of 1 to the point 1 1 and then increases linearly with a slope of 1 from the point 1 1 Answer each of the following questions about f x You have one submission for each question a Does lim f x exist X 3 Yes No c Is f x differentiable at x 3 Yes No e Is f x continuous at x 1 Yes No 1 f Is f x differentiable at x 1 Yes No 2 3

Let f x x a Simplify Computing derivatives using the limit definition f 13 h f 13 h Algebraically simplify your answer until you have cancelled out the factor of h in the denominator Hint See Problem 9 on Assignment 2 2 for similar computations b Evaluate lim f 13 h f 13 h 0 h If an answer does not exist enter DNE y c Determine the equation of the line tangent to y f x at x 13

Given lim f x 2 and lim g x 1 evaluate 8118 8178 lim g x ln 6f x 4 8118 lim 8118 lim 8118 lim 8118 69 x e f z 6 2 49 x cos f x a x C

Suppose a student finds the following values of x and f x x If f 4 9 3 4 99 877 C 4 999 2393 these values would SUPPORT the claim that lim f x x 5

Evaluate the limit 4 6x lim I 11 4x Use oo if the limit is and oo if the limit is

Suppose lim f x 8 Find the following Type DNE if the limit does not exist 48 2 lim 8 f x 8 2 lim 2 8 f x 8 2 lim z 8 f x 8

Suppose a student finds the following values of x and f x X 2 9 f x 5 If f 2 99 971 2 999 8884 these values would make us DOUBT the claim that lim f x

B x y 11 Determine the exact values of cos I 4 TC 4 T 9 Use the diagram above to approximate the values of cosand sin 4 A 1 0 10 Use a calculator to find the values of cos and sin 4 4 and sin 4 12 Compare your answers to 9 11 What would account for any differences

Suppose lim f x 7 lim g x 3 x x x f x 5x 3 3x 1 lim 4 xxxg x

Write a recursive rule for the sequence 208 104 52 26 13 6 5 A recursive rule for the sequence is a a

Curriculum 2 0 Precalculus Unit 3 Topic 1 SLT Evaluating Trigonometric Functions B x y TC G 6 7 Determine the exact values of cos A 1 0 5 Use the diagram above to approximate the values of cos TC 6 Use a calculator to find the values of cos and sin Name Aman Date cosand sin

You create a post on a social media site and tag five friends In the second round each of your friends tag five people and the process continues a Write a function that represents the number of people who are tagged in the nth round an b In which round will 3 125 people be tagged

List the angles of each triangle in order from smallest to greatest 1 7 5 3 4 2 6 A 25 21 13 N 6 38 28 R 26 O

7 P 7 cm R 13 cm 11 cm 8 5 5 ft M 6 ft 1 ft N 9 Q 1 9 cm s 4 1 cm 4 0 cm R

13 50 40 30 14 28 21 20

A website has 400 000 members The number y of members increases by 9 each year a Write an exponential function that represents the website membership after t years b How many members will there be after 3 years Round your answer to the nearest ten thousand a y b about memboro

The lengths of the sides of a triangle are given Classify each triangle as acute right or obtuse 10 21 15 8 11 20 16 12 12 6 5 4

List the sides of each triangle in order from shortest to longest 2 B 41 56 0 3 75 107 R

The value of a car is 27 300 It loses 12 of its value every year a Write a function that represents the value y in dollars of the car after t years y b Estimate the value of the car after 5 years Round to the nearest dollar