Vector Calculus Questions and Answers

Identify the statements among a h that follow directly from the given condition about x The graph of y 2 cosx has a relative maximum at X a cscx is undefined b sec x is undefined c The graph of y secx has a relative maximum at x d The graph of y cscx has a relative minimum at x e The graph of y secx has a vertical asymptote f The graph of y cscx has a vertical asymptote g The graph of y cscx has a relative maximum at x h The graph of y secx has a relative minimum at x

Give the equation for the function which would have graph shown below Use f z for the output

ADS equal to A 273 degrees F B 273 degrees C C 273 degrees F D 273 degrees C

A C Find the graph of the function y cos x 2 B P D 1

Find Singular Value Decomposition SVD of a given matrix Let a 1 and b 0 A b a a b b a b a Please explain the solution steps in detail

Identify the polar coordinate that is not equivalent to O O 3 3 3 3 11T 6 6 7 T 6 5T 6 3 19m Previous 3 57 6

Evaluate 6 7i 4 3 6i 1 O 62 46i O 22 46i O 22 74i

Which of the following graphs is the correct plot of y 4 5 2 5 4 3 2 123 2 2 2 3 5 3 2 3 4 a st 4 sin x 5 5 3 2 He 3 5 2 3 5

Which function represents y tan x A C 2 1 1 201 T B D T

Find the quotient 6 cos 5m i sin 5m 3 cos 2m i sin 2 A 2 cos 3m i sin 3m B 2 cos 7m i sin 7m C 2 cos 3m i sin 3m D 2 cos 7m i sin 7m

What is the magnitude of w 8 3 13 W Round to the nearest hundredth Enter

B Find C in degrees C a C b A A 29 b 4 C 10 C degrees Round to the nearest tenth Ente

Below is the graph of the function dog ar with points given by y dog ar Do the followin Sketch the graph of the function pup x defined by the equation pup z dog x 2 on the same coordinate grid 8 points State the domain and range of dog a below 2 points State the domain and range of pup r below 2 points P Domain of dog x 00 da P dog 2 1 Domain of pup r

Find the ation of the quadratic function g whose graph is shown below LLL 8 4 5 5 12 14 g x

Graph the parabola y 3x 30x 70 Plot five points on the parabola the vertex two points to the left of the vertex and two points to the right of the vertex Then click on the graph a functio button 10 X C

These are two similar triangles What does x equal 15 7 10 X x 9 Enter

A wall is 15 ft high and 10 ft from a house Find the length x of the shortest ladder whic can go from the top of the wall to a window 20 5 ft above the ground 15 X 20 5 10 x ft Round to the nearest hundredth Ente

The total curvature of the portion of a smooth curve that runs from s So to S So can be found by integrating x from S 4 1 ds Sxds Sxrdt x v dt 0 to So to s If the curve has some other parameter say t then the total curvature is K where to and t correspond to so and s a Find the total curvature of the portion of the helix r t 8 cos t i 8 sin t j tk 0sts 4 b Find the total curvature of the parabola y 3x x a Find the total curvature of the portion of the helix r t 8 cos t i 8 sin t j tk 0 t 4x The total curvature is Type an exact answer using as needed

7 What is the polar form of the given double integral in the Figure 1 x S 0 a e b c Serdrde d e 0 rdrde f 2 e rdrd0 S e rdrdo ferdrde 2 Bos b rak e x 1 dy dx

2 a Let f x y arctan x y and D f P Vf P u Find the 1 direction cos 0i sin 0j for which Duf 0 1 2 15

Find parametric equations for the tangent line to the curve with the given parametric equations at the specified point x t y e t z 4t t 0 1 0 x t y t z t Illustrate by graphing both the curve and the tangent line on a common screen The tangent line will be plotted for 1 t 1 Select Update Graph to see your response plotted on the screen the Submit button to grade your response Update Graph Student Response Response Description 3

Five cards are dealt off of a standard 52 card deck and laid out in order Please circle your final answer a How many different lineups are possible 6 How many lineups have at least one red card c What is the probability that you get at least one red card d How many lineups are either all black or all hearts e What is the probability that all of the cards are hearts

estion 6 5 points X n 2 F 2 1 2 X n what is the even Component of the X n Signal d 1

1 Let g x 3x 2 4 a Identify the transformation in words necessary to obtain the graph of g x from the graph of f x 4 b Graph f x and g x on the axes provided Be sure to clearly label your final function g x Clearly indicate at least three points on each graph and the asymptote of each graph 104 c State the domain and range of g x in interval notation Domain of g x Range of g x d State the asymptote of g x as an equation Asymptote of g x 10 8 6 4 2 8 6 2 24 6

Match the equation with its graph x y z 6

Sketch the curve whose vector equation is Solution r t 2 cos t i 2 sin t j 5tk The parametric equations for this curve are y 2 sin t z X Since x y 4 sin t the curve must lie on the circular cylinder x y The point x y z lies directly above the point x y 0 which moves counterclockwise around the circle x y in the xy plane The projection of the curve onto the xy plane has vector equation r t 2 cos t 2 sin t 0 See this exampl Since z 5t the curve spirals upward around the cylinder as t increases The curve shown in the figure below is called a helix 2 0 0 0 2 57

Use modular arithmetic to find 7 11 9 and 11 x7 5

he mathematical model p 0 01s2 0 8s 3 7 describes the percentage of college students p who are anticipating a starting salary s in thousands of dollars a Use the formula to find the percentge of students who anticipated a starting salary of 40 thousand h Does the starting slaary of 40 thousand have the highest percentage of students Explain

Find the velocity and acceleration vectors in terms of u and up de T 2ea0 and 1 dt v u uo V

nd the velocity and acceleration vectors in terms of u and up a0 3e and do dt 2 GTX

If f you already know lal and lvl then the formula a k v gives a convenient way to find the curvature Use it to find the curvature and radius of curvature of the curve r t cost t sin t i sin t t cos t j t 0 The curvature is

Show all work No Calculator is allowed 1 Graph one cycle of the graph of f Label the intercepts and the high low points F x 5cosx 6x n 2

36 You have a wire that is 71 cm long You wish to cut it into two pieces One piece will be bent into the shape of a right triangle with legs of equal length The other piece will be bent into the shape of a circle Let A represent the total area enclosed by the triangle and the circle What is the circumference of the circle when A is a minimum

If Ps is a monic quintic polynomial for which Ps 2 cost 2 cos 5t for all angles t then A Ps x x 5x 5x B Ps x 3x 5x C P x x 5x I D Ps x x 6x 4x E Ps x x 7x 3x

a Sketch the region bounded by y x y x 10 b Find the area of the bounded region J x dx f vdx 32 2 4 4 un units X X x X x x 0 x x 1 0 X 0 1 7 6

Use the Midpoint Rule with n 6 to approximate th T dr

Consider the function y 4 sin 2x 7 Give exact answers using fractions and multiples of Determine the following information a Amplitude 4 b Period T c Phase shift Direction Left Number of units enter a positive number using fractions and multiples of 5 0 d The point 0 0 transformed into e The point 5 transformed into 0 0 f Graph the function 57 8 122 32 8 Clear All Draw ww X 4 2 3 4 54 T 2 A 718 T14 31 8 2 57 8 3TV

OSCAGC03s02q512P What is the domain of the function O 0 11 O 0 2 O 1 1 00 0 0 7 O f x 3 7 2x

Find a complex vector d so that if F fo f1 2 3 f2 F 0 fi f2 0 c then F

What is the sub reference function f x for the function f x 5 x 3 2 4 the function that handles the non rigid transformation of the parabola first O f x 5x 0 x x O f x 5 x 3 O f x x 3

Plot the vector field F ri y j Now consider the points P 1 5 0 5 and P 1 5 0 5 Identify whether these points are sources or sinks Using the definition of divergence verify your answer

Consider the following equations 2 2y 4x 3 x y and y 5 6 7x Step 1 of 3 Express the first equation in slope intercept form Simplify your answer Anguo

Find the orthogonal projection of v projection onto the plane 2x1 x2 3x3 0

The position of a particle in the xy plane at time t is r t t 4 i t 3 j Find an equation in x and y whose graph is the path of the particle Then find the particle s velocity and acceleration vectors at t 5 CHICKLICHE The equation for the path of the particle is y x 8x 13 The velocity vector at t 5 is v Simplify your answers

10 A restaurant has a main location and a traveling food truck The first matrix A shows the number of managers and associates employed The second matrix B shows the average annual cost of salary and benefits in thousands of dollars Complete parts a through c below Managers Associates 5 21 1 4 Restaurant Food Truck a Find the matrix product AB AB A Managers Associates Salary Benefits 7 42 20 4 B Simplify your answer b Explain what AB represents Choose the correct answer below OA Row 1 of AB represents the restaurant and row 2 represents the food truck Column 1 of AB represents total salary in thousands and column 2 represents total benefits in thousands for all employees OB Row 1 of AB represents the restaurant and row 2 represents the food truck Column 1 of AB represents total benefits in thousands and column 2 represents total salary in thousands for all employees OC Row 1 of AB represents the food truck and row 2 represents the restaurant Column 1 of AB represents total benefits in thousands and column 2 represents total salary in thousands for all employees OD Row 1 of AB represents the food truck and row 2 represents the restaurant Column 1 of AB represents total salary in thousands and column 2 represents total benefits in thousands for all employees c According to matrix AB what is the total cost of salaries for all employees managers and associates at the restaurant What is the total cost of benefits for all employees at the food truck The total cost of salaries for all employees at the restaurant is The total cost of benefits for all employees at the food truck is

Find the dimensions of the rectangular field of maximum area that can be made from 220 m of fencing material A 110 m by 110 m B 55 m by 55 m C 22 m by 198 m O D 55 m by 165 m

For the function f x 3x 2 4 find f x f 0 f 2 and f 3 f x

Verify the Divergence Theorem for the field F x y z 27i z k over the solid cylindrical shell 1 x y 4 0 z 4

Find the slope m of the line through P 2 6 and Q 5 21 m Enter a fraction integer or exact decimal Do not approximate

Let x 2 2 1 2 4 be a circle Find its equation and image under the effect of shear parallel to x axis by factor 2 draw the graph Answer in detailed every step Linear Algebra