Vector Calculus Questions and Answers

OSCAGC03s02q520P What is the domain of the function O 3 00 O 3 00 O O 3 O 3 00 f x 4 T 3

42 MAR ECTION B APPLICATION If h x log x 2 3 6 marks graph h x and h 1 x on the grid provided labelling all asymptotes the tion of the inverse etermine the equation of

3 25 pt Minimize the function f x y z x 2y2 z2 subject to the constraints x y z 0 and x z 1 by using Lagrange multipliers

Show that the method given by the Butcher tableau has order 2 for any 1 1 0 d 8 1

d and sketch the domain for the function sin xy y 16 f x y Choose the correct description of the domain below A All x y satisfying xy nx for integer n OC All x y satisfying x y2 16 20 2 OE All x y satisfying x y 16 0 2 OG All xy satisfying x 16 or y 16 O B All x y satisfying x y 16 0 I OD All x y satisfying xy n O F for in All x y satisfying x 16 and y O H All x y satisfying x y 16 2 16 0

b Use the formula in part a to find the distance from the point P 1 1 1 to the line through Q 0 7 7 and R 1 3 6

What is the direction of w 12 4 113 degrees Round to the nearest hundredth Enter

Which function represents y sin x At A B D AA 14 2 IAA

Find the vector not with determinants but by using properties of cross products k x k i

Select all equations with unique solution 5 2 3 6 b 8 0 0 Axb where A 5 2 4 679 0 5 3 b 3 Axb where A 0 Ax b where A 0 Ax b where A 0 4 25 7 0 3 0 4 0 0 0 5 5 3 3 0 5 0 b 2 0 0 4 0 79 3 9 0 5 2 5 b 3 2 5 3 4 0 0 0 5 Axb where A 0 Axb where A 0 0 5 3 Axb where A Ax b where A 0 2 5 5 0 2 0 4 4 0 0 0 0 0 2 3 4 5 3 3 0 5 0 0 0 4 0 0 0 4 b b 2 0 2 4 0 3 0

Find the area of this triangle 11 13 25 square units Round to the nearest tenth Ente

How many periods are shown in this graph 2 10 2T 4T

B Find the length of side a A a b C B 60 b 7 c 3 a units Round to the nearest tenth

Evaluate the cube root of z when Z 8cis 77 4

6 5 4 3 2 1 1 0 1 2 3 2 3 4 What is the component form of v 5 V 6 7 8 00 Question

Find the period of this function y sin 10 1 2 T

With v 33 ch and w choose a number e so that w ev is perpendicular to v What is the formula for e starting from any nonzero v and w Use to indicate dot product

Let f be a Riemann integrable function on 0 1 Li 1 2 m x dx 0 i Let g be in 0 1 Find lim n g ii Is the answer the same if g

v 60 u 90 40 20 w 40 30 What are the magnitude and direction of u v w Round the magnitude to the thousandths place and the direction to the r

Give the domain and range for the function shown below Use 10 9 8 7 6 5 4 3 2 Domain 4 6 Range 10 5 1 10 9 8 7 6 5 4 3 2 1 2 3 4 567 8 9 10 1 2 3 4 5 6 7 8 9 10 X X a

Find the magnitude and the direction of the resultant vector A 16 6 57 3 B 12 48 4 C 16 6 32 7 D 12 41 6 5 11 w 4 3

The table gives the height as time passes of a typical pine tree grown for lumber at a managed site Tree age years 20 Height feet 13 t 10 If H t is the height of the tree after t years construct a table of estimated values for H Use a one sided difference quotient with an adjacent point for the first and last values and the average of two difference quotients with adjacent points for all other values Round your answers to two decimal plac 14 21 05 28 35 Sketch the graph of H H 42 49 H t 14 14 21 28 40 54 35 42 49 64 72 79 84 42 49 H 20 15 O 10 Cast 14 21 28 55 A 49 15 10 031 19 K 21 35 42 49 1 A 201 15 10 031 14 L 35 L

Write the equation of the sphere in standard form x y z 6x 2y 6z 3 Find its center and radius center radius x y z

Use the given points to answer the following questions A 4 0 2 B 3 2 4 C 2 4 6 Which of the points is closest to the yz plane A B C Which point lies in the xz plane OA OO B

Find a b a 3 1 b 7 4 4

Simplify O y 9y y 7 y 13y y 7 y 14 3 7 y2 13y 14 y 7 4y 14 y 7 y 5y 14 y 7

The diagram shows a cube where AB AD 7 and AE 13 E A u B F H G C A single vector equivalent to v w is O a BH Ob DE OC CE O d AG

c Determine the exact value of x 5 5 Hint First find the Mclaurin series for e

Two sectors of the U S economy are 1 audio video and communication equipment and 2 electronic components and accessories The input output table for the two sectors was as follows all numbers are in million dollars Equipment Components Total Output Build the technology matrix Equipment 6 030 24 030 90 000 Components 560 29 960 140 000

Find the horizontal and vertical components of this vector k 55 Round to the nearest tenth V 10

Find a function of the form 3 A sin kr Cor y A cos kx C whose graph matches this one n 14 in S 4 A Leave your answer in exact form if necessary type pi for

Suppose that W W and W are wffs in the Propositional Calculus such that the following sequent is valid W W Which one of the following sequents is valid W W W W F W W W W OW W W W O W W F W W TTT TIT

9 sin x 3cos x sinx 3 COSX O SCOX X 3 COS X 0 1 5707 X 1 209 Gno 3 points 10 2015 X no solution

Without graphing the function y 7 cos 9x determine its amplitude and period Leave answers in exact form type pi for amplitude period

Graph the following function over the indicated interval y 2 3 3 Choose the correct graph below O A 10 Ay Q OB 4 10 Ay G C O C 4 Ay Q 3 O D

The graph of y f x is given Graph the function y 23 7 6 5 4 w 6 5 4 m A 5 6 y f x 2 3 4 5 6

Find all y intercepts and x intercepts of the graph of the function f x x 2x 35x If there is more than one answer separate them with commas Click on None if applicable y intercept s x intercept s 8 None 0 6 2 16 30 0 X 3

Question 5 Use diagonalization to compute the indicated power of the following matrices 1 01 a 1 6 b 2 2 2 Lo 1

What is the direction of w 8 3 K 13 degrees Round to the nearest hundredth Entor

Use the graph y g x to graph the given function 7 6 5 4 3 2 1 2 3 5 4 7 2 y g x 2

Consider the graph of the function f x x 6X 7 x 2x 63 What are the vertical asymptotes List the x values separated by commas Provide your answer below

Write the vector shown below as a combination of vectors u and shown above Vector u u Note In both graphs each box is 1 unit by 1 unit in size

5 Find the expected value for the random variable x having the probability function shown in the graph X P x Complete the probability distribution table below Simplify your answers Type integers or decimals 1 Find the expected value E x 2 3 AP 0 3 0 25 0 2 0 15 0 1 0 05 0 4 1 2 3 4 5 Simplify your answer Type an integer or a decimal 5 X

Use the indicated entry inside the brackets as the pivot and perform the pivoting process once Do not solve X1 X2 1 2 Z 1 2 1 1 8 0 0 6 8 0 1 0 8 12 0 0 1 O x1 x2 51 52 z 1 2 1 2 0 2 0 O x1 x2 1 2 1 20 4 0 O x1 x2 1 2 1 2 0 2 0 1 8 0 0 7 1 1 0 16 3 2 0 1 84 51 52 z 1 8 0 0 7 1 1 0 16 3 2 0 1 84 720 1 2 z 1 8 0 0 7 1 1 0 16 3 4 0 1 84 O x1 x2 51 52 Z 1 2 1 1 8 0 1 2 0 1 0 7 0 12

Solve the problem Burger Barn s three locations sell hamburgers fries and soft drinks The matrix that displays daily sales figures for all locations is Barn I Barn II 1500 950 900 Burgers 900 Fries 600 Drinks 750 Burgers cost 1 50 each fries 0 90 an order and soft drinks 0 60 each The matrix that displays the prices is 1 50 0 90 0 60 What matrix displays the daily revenue at each of the three locations Barn I Barn II 2340 3645 Barn I Barn II 2540 3645 Barn I Barn II 2340 3785 Barn I Barn II 2340 3645 Barn III Barn III 1150 800 825 2760 Barn III 2940 Barn III 2940 Barn III 2940

Set up the system of equations Do not solve An investment firm recommends that a client invest in bonds rated AAA A and B Let x be the number of AAA bonds y the number of A bonds and z the number of bonds The average yield on AAA bonds is 4 on A bonds 6 and on B bonds 12 The client wants to invest twice as much in A bonds as in B bonds How much should be invested in each type of bond if the total investment is 35 000 and the investor wants an annual return of 1940 on the three investments Ox y z 35 000 4x 6y 12z 194 000 2y z 0 O x y z 35 000 4x 6y 12z 19 400 x 2z 0 Ox y z 35 000 4x 6y 12z 194 000 y 2z 0 Ox y z 35 000 4x 6y 12z 194 000 x 2y 0

Graph the feasible region for the system of inequalities 2x y 4 x 2y 4 O O 3 x 21 P 5 4 3 2 1 3 1 5 4 3 2 1 1 2 3 4 5 2 3 1 1 2 3 4 5 x 3 2 5 4 3 2 11 1 2 3 4 5 x 2 3 1 3 4 5

Write the solution from the final simplex table X1 X2 1 2 Z 0 1 300 24 2 0 1 1 0 16 0 0 1 0 1 200 O 1 0 2 24 S1 0 216 z 200 O 1 0 x2 16 s1 0 52 24 z 200 O 2 2 24 5 0 5216 z 200 01 24 2 16 S1 0 2 0 z 200

Consider the graph of the function f x x 9 x3 2x 15x What are the vertical asymptotes Just list the x values separated by commas Provide your answer below

Consider the graph of the function f x Which is a removable discontinuity for the graph Select all that apply Select all that apply x 2 x 1 x 0 x 1 x x 2x x x x 2