Limits & Continuity Questions and Answers

Evaluate 2x de Question Help Video 1 Vider

Find x where 0 x 2 sinx cot x 1 F TZT

Find the amplitude of this function in 2

Show that there is a root of cos x AHIR in the interval 0 7 TT d the root Explain all of your steps and reasoning and name

Find the horizontal shift y 2 cos x 4 Enter either or Er

The simple interest formula I Prt where Total cost I interest P amount 1 C pq where C total costs P price per unit g quantity Coin Value Name penny nickel dime quarter 7 interest rate t time Value cents borrowed invested 5 Value dollars 0 05 0 10 4 You invest x dollars at 5 percent annual rate for 2 year How much is the simple interest 5 You bought y pounds of apples at 1 75 per pound How much did you pay for the apples 6 You have x dimes and y nickels in your pocket In all how many coins were in your pocket What is the total value in cents of the coins

A C Which of the following represents y CSC X U t U n An UNI 2 Fat at B D X V Za k n th I U U FR 2 t

A cosine function has an amplitude of period of horizontal shift of 2 and vertical shift of 3 What is the y value of the negative function when x y Enter

How many periods of the function y cotx are there between 87 and 2 periods

Find the period Simplify your answer 3T 4 1 57 24 T 7T Enter

Find an equation for a cosine function having an amplitude of 2 period of T horizontal shift of 2 to the right and a vertical shift of 3 y cos x Enter

3 Find the limit X lim tan 6 X

If the rate of change in the microwave rays M x where x is the distance decreases with a rate that is inversely proportional to the square of the number of microwave rays write the differential equation that describes the rate of change of the oven temperature given a distance x Do not solve

Find an equation for a positive cosine function with an amplitude of 4 a period of 87 and a horizontal shift of 2 to the right y cos X Enter

If the rate of change of N is inversely proportional to N x where N 0 If N 0 10 and N 2 5 Find k the proportionality constant N

Use the graph the answer the question y 5 4 3 2 1 5 4 32 3 2 1 1 2 3 1 P 2 3 4 5 Find the y coordinate for the point on the graph where x 3

X X 2 Write each number as an imaginary number a 100 Write your response here b 4 Write your response here

Use the graph the answer the question y 5 4 3 2 1 LO 5 4 3 2 1 1 2 3 41 1 type your answer Give the coordinates of the point P P 2 3 4 5 X

B a Find the length of b C b B 76 a 7 C 12 A C b units Round to the nearest tenth Ente

If a population of buffalo are becoming extinct Assume that 150 years ago there were 100 000 buffalo and that the rate of loss of buffalo is proportional to the population at a given time If there are 4 000 buffalo remaining how many years will it before there is only one left Let P t be the number of buffalo and t measured in years Round to the nearest year

2 Other Representations For each of the following functions describe the input values output values and the rule that relates an input value to an output value a Symbolic Formula Equation Consider the function represented by the following formula F C 32 15 Input values Outout values Rulo Rewrite C as a function of Is this a different function Are the input values output values and rule different Graph Consider the function represented by the following graph GOREN TERES 1500 TERMI HERE Input values

Find a in degrees 7 XX 15 Round to the nearest hundredth Ente

Use the table to find f 1 X 2 1 0 1 3 5 9 f 1 f x 1 2 1 9 5 0 3

Which point is not on the graph of y cSc x A 3 3 B 5 2 2 3 2V3 34 2

Which function represents y sin x A 2 A 27 2 1 10 2 It B D 2 27 2

Rewrite the radical using the imaginary unit 24 O 2i 6 O i 24 O 4i 6 F

How many periods of the function y tan x are there 7 between 7 and 11

If f x 2x 5x find f 3 Oa 6 5 3 Ob 12 5 3 c 11 3 d 7 R

Problem 6 10 points State two vertical asymptotes of the graph of the function f x 3 tan 2x 4

Evaluate the limit using L Hopital s rule 3x e r lim H X Question Help Video Message instructor

Write each number as an imaginary number a V 100 b 4 11 0 1001 You are incorrect 0 41 CV 81 You are incorrect You are incorrect X X X

12 11 10 9 8 7 6 O V 5 4 u 2 7 2 7 5 6 7

Express the following equation as a function y f x if it is possible y 9 x O Impossible because it is not a function Of x x 9 Of x x 9 Of x x 9

8cis 77 Evaluate the cube root of z when z 8cis

1 The total resistance Z in a circuit is given by Z three decimal places Z 2 Z Z where z 70 40i and Z2 50 35i What is the total resistance in standard form Round to

Vectors u and v are shown in the graph u

Simplify the expression and enter the simplified answer in the blank To enter the square root of an expression enter use sqrt as in sqrt3 for 3 3 24 4 54 6

h Evaluate the following limits a lim I b lim H X LO 5 e 7 LO 5 e 7 NOTE If needed enter oo for o and oo for

Given the parametric equations x 5cos 8 and y 5sin 8 which of the following represents the curve and its orientation 8 7 6 7 N 7 3 2 1 1 0 1 2 L 1 2 3 4 6 7

6 Iff and g are continuous functions with f 13 4 and lim 2f x g x 13 find g 13 x 13

Evaluate the limit lim H X 4x 9x 5 2x 9

6 Q Y T R 3 2 1 3 2 1 0 2 3 1 2 3 4 11 Which point is represented by 6 cos 6 T isin Real axis 5 6 7 117 6 S

Question 8 0 1 pt 3 98 i Details Find the magnitude of 3 5i Question Help Message instructor Submit Question the nth root theorem To find the nth root of a complex number in polar form use the formula given as where k 0 1 2 3 n 1 We add 1 2 r cos 2kT isin 27 n n n 2k n to in order to obtain the periodic roots

a Find the slope m of the tangent to the curve y 5 5x 2x at the point where x a M b Find equations of the tangent lines at the following points 1 8 y y c Graph the curve and both tangents on a common axis y 10 2 9 O 5 15 10 5 10 15 X 30 10 5 y 20 15 10 10 5 10 00 10 5 y 10 10 15 10 15 X 09 10 5 y 201 15 10 10F 5

6 Which three points are on the plane 2x 7y 3z 5 0 P 4 3 6 2 0 0 0 and R 3 1 2 b P 1 0 1 Q 2 2 3 and R 3 1 2 P 1 0 1 Q 3 1 2 and R 4 3 6 d P 3 1 2 Q 4 3 6 and R 5 0 2 27 What is the vector equation of the line with parametric equations x 2t 7 y 3t 2 t R 7 2 s 2 3 s eR c 7 2 7 s 3 2 SER b r 2 3 s 7 2 s R d none of the above

What is tan 45 2 A 1 tan 45 1 Ente

Suppose y is a function of z and function f represents this relationship A table of values for zand f z are shown below f 14 b Evaluate f 9 f 9 c Solve f x 5 for z z f z 2 722 2 79 6 Answer each of the following questions If there is more than one answer enter your answers as a comma separated list If there isn t enough information to answer the question enter DNE a Evaluate 14 5 13 5

ce or copy the graph of the given function f Assume that the axes have equal scales Use estimates of the derivative of f to sketch the graph of f on the same coordinate aves y

2x 34 8 n k 2 am 1 1 C 8 6 1 224 8 5 4 8 4 2x4 4 34 4 4 16 x 3 702 70 162 16 8138 907202016 34 8 38 bk 1 34 0 2 c s GS 3 G

The graph below is the function f x 3 2 1 5 4 3 2 1 1 2 3 4 5 1 2 3 4 5 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 I 2 f x exists lim f x f 2 2 2 The function is continuous at x 2 The function is not continuous at x 2