Differential equations Questions and Answers

Evaluate the definite integral 32 88 3x 3x 1 dx X

8 1 3 8 and 3 1 cep 1 of 2 Determine whether or not the given points form a right triangle If the triangle is not a right triangle determine if it is isosceles or scalene answer O Right Triangle O Isosceles Triangle Keyl

19 A ball is thrown straight down from the top of a 230 ft building with an initial velocity of 30 ft per second The position function s t 16t vot so What is the velocity of the ball after 3 seconds a The velocity after 3 seconds is 78 ft per second b The velocity after 3 seconds is 66 ft per second c The velocity after 3 seconds is 126 ft per second d The velocity after 3 seconds is 18 ft per second e The velocity after 3 seconds is 252 ft per second

10 Find the x values if any at which b f x is not continuous at a f x is not continuous at x 0 and f x has a removable discontinuity at x 0 x 0 1 C f x is not continuous at x 1 f x x x is not continuou d f x is not continuous at x 0 1 e f x is continuous for all real x and both the discontinuities are nonremovable x 1 and f x has a removable discontinuity at and f x has a removable discontinuity at x 0

Use the Midpoint Rule with n 4 to approximate the integral 12 2 x 0x dx M

2 In 3x 3 2x Find the derivative of the function y

Solve the following initial value problem for r as a function of t Differential equation Initial condition dr 4 tan t i r 0 4i 3j k dt TU 12 s j sec 3t k t 6

2 Evaluate antation So 706 cos 3 dz where C denote the unit circle with positive ori

Find all values of x such that sin 2x sin x and 0 x 2m Enter your answers as a comma separated list If you have had difficulty with these problems you should look at Appendix D of your text

Convert from radians to degrees Round your answer to one decimal place 8

Simplify the rational expression x 9x 18 x 3x 18 If you have had difficulty with this problem you may wish to consult t

Solve the inequality Write your answer using interval notation 4 3 7x 31

Simplify the expression Write your answer without negative exponents 300 48 If you have had difficulty with this problem you may wish to consult the Review of Algebra on the website

O This is the correct answer This answer is incorrect ct answer

Questions Numerical questions require you to enter a number Type the correct answer into the answer box To have WebAssign grade your answer click Submit Answer A mark is displayed to indicate whether your answer was correct 1 1

44 Find the critical numbers of f x 3 2x x

15 points Solve y 2y 5y 6y 12xe 2e y 0 2 y 0 7 y 0 9 using the method Laplace transforms Feel free to use the appropriate table and formula

Describe how each of the following is translated 1 X 2 1 0 1 f x 1 2 4 1 2 2 3 4

Find the area inside both the polar rose r 4sin 20 and the curve r 5 2 sin 20 in the first quadrant Enter an exact answer

Use the Alternating Series Remainder Theorem to determine the smallest number of terms required to approximate the sum of the series with an error of less than 0 001 1 1 04 S n 1

Determine the convergence or divergence of the series 8 sin 2n 1 n 1 O converges O diverges

nd the indefinite integral Use C for the constant of integration 2 x 2 3 2 dx ADANO

Perform the multiplication and use the fundamental identities to simplify There is more than one correct form of the ans 8 8 sin x 8 8 sin x Step 1 First multiply out the two factors Step 3 64 64 Step 2 Simplify the expression obtained 64 sin x Factor 64 64 64 sin x 64 a 64 64 sin x 64 sin x sin x

Question 5 True of False The magnitude of 2v is shorter than the magnitude of v A B True False G Jay

find all the local maxima and the Local minima and saddle points Of function 3 f x y x y 3x 9y 6

Find the equation for the plane through the point Po 0 2 5 and normal to the vector n 3i 6j k Choose the correct answer below OA 3x 6y z 7 OB 3x 6y z 0 OC 3x 6 y 2 z 5 0 OD x 3 2 y 6 5 2 1 7

Find the distance from the point 3 5 4 to the a xy plane b yz plane c xz plane a The distance from the point to the xy plane is Type an exact answer using radicals as needed

Sive a geometric description of the set of points in space whose coordinates satisfy the given pair of ec 2 2 z 4 y 2 Choose the correct description A The line that passes through the points 2 0 2 and 0 2 0 OB The line through 2 2 2 parallel to the y axis OC The circle with center 0 2 0 and radius 2 parallel to the xz plane center D The circle with center 2 0 2 and radius 2 parallel to the xy plane

Find dy dx by implicit differentiation xy x y 67 dy dx

15 pnts Let F x y z ye e i e j xe k be a vector field a Find curl F and div F b Is F a conservative vector field If yes then find potential func tion

Solve the Chebyshev equation by the Frobenius method

12 Determine the domain and range of the function 5x 2 x 0 f x 5x 6 x 0 a b d 2 2 n 6 2 U 6 x le domain range C domain c range domain 2 U range domain range 2 U 6 5 2 n 6 domain range

10 Evaluate if possible the function a 8 39t 72 b 8t 57t 72 c t 14t 57t 72 d 3 14 39t 72 e none of the above g x x x 5 x t 3 at Simplify the result

7 Write an equation of the line that passes through the given point and is parallel to the given line Line 3x 7y 9 Point 2 1

Use the chain rule to find dz dt dz dt z V2 xy x tan t y arctan t 1 arctan t tan t 2 3

Find parametric equations for the line Use the parameter t the line through the origin and the point 9 7 1 x t y t z t 3 9 1 Find the symmetric equations X 9 y 7 z 1 7 2 1 17 2 9 11 12 11 12 2 XY 9 7 X 9 y 7 z 1 7 7 1 2 2 9 X

Find all the angles in AABC if side a 24 9 cm side b 15 3 cm side c 28 0 cm

4 6pts Solve the following equation log x 7 log x 8 1

F s 3s 165 15 s 3 Ans f t 3e 3t 2te 3t 3t e 3t

2 Use the following graph of f x to answer the following questions a f 1 b lim f x X 1 c f 4 d lim f x X 4 2

Given the graph of y f x below find the value f 2 Provide your answer below 6 5 4 3 2 3 3 4 in 6

Given the graph of y f x below solve for f x 2 6 5 4 1 4 199 4 6

Is the following scenario a combination problem or a permutation problem A group of 25 people are going to run a race The top 8 finishers advance to the finals Select Select Combination Permutation

Consider the following function f x x 1 5 2 a Find an equation of the tangent line to the graph of fat the given point y b Use a graphing utility to graph the function and its tangent line at the point 10 101 b S 10 15 20 10 15

The graph shows how the average surface water temperature f of Lake Michigan varies over the course of a year where t is measured in months with t 0 corresponding to January 1 The average was calculated from data obtained over a 20 year period ending in 2011 f F 70 60 50 40 0 2 4 6 8 10 12 t months

Simplify completely assuming both x 0 and y 0 64x7y10

Simplify completely assuming both x 0 and y 0 81x 2y7 Select the correct answer below O 3x yvy O 27x4y x y O 27x4y 3xys 9x y y5 O 3x4y xy O 3x y y

have a tangent line that is nearly horizontal v of must have a tangent line that is nearly vertical I y 2 c x 1 2 RHS xy 4 x 2 c x2 1 213 4 TQ y X and hence y is close to 0 If x is large then xy 4 is large Thus the graph of y m and the gra In both cases we assume reasonable values for b Verify that all members of the family y 2 c x 1 2 are solutions of the differential equation y xy 4 c x2 3 2 c x2 3 2 y LHS c Graph several members of the family of solutions on a common screen y WebAssign Plot V 6

d Find a solution of the initial value problem y xy y 0 4 4 y

Solve the simultaneous differential equations using Laplace transform b dx dy dt dt 2x e t dx dy 3 dt dt given that r x 4 cost Jand 0 when t 0