Calculus Questions

Use a substitution to find 0 7 0 It 150 13 S cos 2 de x cour dix

Use a substitution to find f sin x cos xdx O cos zsin x C 6 sin z cos x C OCCO E C in 2 C

Use the integration by parts formula to find freda Show your work and final answer in the provided area using HTML Editor s Insert Math Equation function Edit Format Table 12pt Paragraph BIUA 2 T

Find the arclength of y 2x 2 on 0 x 3

Find the surface area of revolution about the x axis of y 2 sin 5x over the interval 0 x 5

Let f x 3 log x f x f 8 3 In 3 x 3 In 24

9x 9 x10 10 Hint Use In properties In u v ln u ln v ln ln u ln v and ln u p ln u Find the derivative of In 10

If f x 2 cos 4 ln x find f x 8 sin 4 In x Find f 5

The force on a particle is described by 9x 6 at a point x along the x axis Find the work done in moving the particle from the origin to x 9

Find the arclength of x 2y 2 on 2 y 9 to three decimal places

Find a z score such that 63 of the area under the standard normal curve is below that score Click the icon to view the area under the standard normal curve table

The 2022 sophomore PSAT scores are normally distributed at East Richmond Hills High School with an average or mean score of 600 and a standard deviation of 25 What is the probability that a randomly chosen sophomore at East Richmond Hills earned a score less than 600 on the PSAT this year

Write cos F 00 11 in terms of the cosine of a positive acute angle Provide your answer below

Question The terminal side of angle intersects the unit circle in the first quadrant at y What are the exact values of sin cos 0 Provide your answer below

16 Does the relation is less than for numbers have a reflex ive property consider one number A symmetric propert consider two numbers A transitive property consider three numbers

Use a reference angle to write sin Provide your answer below 31 36 in terms of the sine of a positive acute angle Include parentheses in your answer 31

Question Determine the exact values of sin 0 and cos 0 given that the terminal side of angle 0 intersects the unit circle in the first quadrant at Provide your answer below

If the terminal side of angle 0 goes through the point 3 3 2 3 13 13 Provide your answer below on the unit circle then what is sin 0

Question Find an angle A that is coterminal with an angle in radians measuring 23 where 0 A 2 Give your answer as an exact answer involving if necessary

The graph of f is shown in the figure to the right Let A x f t dt and 2 X F x f t dt be two area functions for f Evaluate the following area functions 4 a A 2 b F 8 c A 4 d F 4 e A 8 a A 2 0 Simplify your answer b F 8 9 Simplify your answer Area 9 Area 16 Area 91

An arch is 615 ft high and has a 560 ft base It can be modeled by the parabola 27 X y 615 1 0 Find the average height of the arch above the ground 280 700 600 700 400 300 200 100 400 200 0 200 400

REAL NUMBERS Finding the sale price without a calculator given the original pri The price of an item has been reduced by 65 The original price was 20 What is the price of the item now

A student takes a multiple choice test of 20 with four choices and guesses on each question Find the probability that the student gets exactly 6 correct answers 0 1686 O 0 3819 0 0745

Graph the function g x log x 3 2 O O O 3 3 1 2 1 3 3 3 6 X

Write and equivalent algebraic expression that involves x only tan sin 1 7 x

Identify the x intercepts of the parabola y x 1 16 O 3 0 and 5 0 O 2 0 and 4 0 O 0 3 and 0 6 O 3 0 and 5 0

Use the product quotient and power rules of logarithms to rewrite the expression as a single logarithm 2 loga x 3 log y 5 loga z O loga x2y6 25 x2 loga y5 5 O x2y8 z5 x2y5 10Ba

Solve the exponential equation 37 3 243 Ox 3 Ox 2 3 x 2 3 Ox 4

Find the vertical and horizontal asymptote s of the graph of the rational function f x 2x 3 x x 6 O Vertical Asymptotes x 1 x 6 Horizontal Asymptote x axis Vertical Asymptotes x 2 x 3 Horizontal Asymptote x axis O Vertical Asymptotes x 2 x 3 Horizontal Asymptote x axis O Vertical Asymptotes x 2 x 3 Horizontal Asymptote y 2

A car dealership has 7 red 4 silver and 8 black cars on the lot Five cars are randomly selected to be displayed in front of the dealership Find the probability of selecting 2 red 2 black and 1 silver O 0 785 0 202 0 283 0 385 00117

Find the amount that should be invested now to accumulate the following amount Round the answer to the nearest dollar 7400 at 6 compounded semiannually for 8 years O 4700 4611 O 4580 3840 3580

In a club with 8 members how many ways can the club elect a president a treasurer and a secretary 358 O 112 56 336 240

Solve sin x 0 75 on 0 x 2 There are two solutions A and B with A B and A and B in radians to 4 decimal places A B

Let f 2 423 1922 the remaining zeros of f Oax 2 3i and x 3 4 b x 2 3i and x 3 4 r Oca 2 3i and x 2 3i Odx 2 3i and x 4 3 Oex 2 3i and x 3 4 x 2 3i and x 3 4 O 642 39 If it is known that r 2 3i is a zero of f find Of

Using synthetic division determine whether the numbers are zeros of the polynomial function 2 3 2 f x 3x 5x 6x 18 Select the correct choice below and if necessary fill in the answer boxes to complete your choice OA The number 3 is a zero of the polynomial function because f 3 OB Neither 3 nor 2 is a zero of the polynomial function because f 3 OC The number 3 is not a zero of the polynomial function because f 3 OD Both 3 and 2 are zeros of the polynomial function because f 3 0 and f 2 0 4 and the number 2 is not a zero of the polynomial function because f 2 and f 2 and the number 2 is a zero of the polynomial function because f 2

completely factor p x into linear functions zero 3 i p x x 4 6x 3 46x 2 216x 360

a x y Solve the system u 2x y v 2x 2y for x and y in terms of u and v Then find the value of the Jacobian Find the image under the transformation of the triangular region with vertices 0 0 2 4 and 2 2 in the xy plane Sketch the transformed region in the uv plane a u v The function for x in terms of u and vis x The function for y in terms of u and v is y The Jacobian of the transformation is J u v 6 0 2u v 6 Av V U 3 Choose the correct sketch of the transformed region in the uv plane below A 0 12 1 6 Q 5 B 0 12 6 0 Q Q GALLE OC 0 12 6 0 Q 9 G OD AV 6 0 0 12 od u

me integrals below give the area of a region in the xy plane Sketch the region label each bounding curve with its equation and give the coordinates of the points where the curves intersect Then find the area of the region TC 4 3 cos x S S 03 sin x dy dx Sketch the region label each bounding curve with its equation and give the coordinates of the points where the curves intersect Choose the correct answer below A OB VES sinx V3 cos x E The area of the region is 3 2 1 Type an exact answer using radicals as needed Ay y 3 cos x 1 3 sin x Q 3x O C x 312 42 y 3 cos x y 3 sin X OU 2

of For the function f x y sin 3x 3y find 7 dx f 6 21 sin 3x 3y cos 3x 3y dx f av 11 6 21 sin 3x 3y cos 3x 3y and of dy

ketch the region of integration associated with the double integral 2 SS f x y dy dx 0x Choose the correct sketch of the described region OA 5 OB 8 13 O OU OD

Setup an integral to find the surface area of a sphere of radius 1 using the surface areal integral formula Do not evaluate the integral Type your integral that you setup in the text box here and include your work in your File Upload

Solve the system u 2x y v 2x 2y for x and y in terms of u and v Then find the value of the Jacobian The function for x in terms of u and v is x The function for y in terms of u and v is y The Jacobian of the transformation is J u v Choose the correct sketch of the transformed region in the uv plane below O A OB 6 0 0 12 Q Q 0 12 6 0 xx y Find the image under the transformation of the triangular region with vertices 0 0 2 4 and 2 2 in the xy plane Sketch the transformed region in the uv plane u v Q GITS OC 0 12 6 0 Q Q OD U 6 0 0 12 O a

8 Sketch a possible graph of a function f showing any vertical asymptotes or holes and that satisfies all of the follow f 0 1 f 4 is undefined lim f x 1 18 lim f x lim f x DNE lim f x 88 lim f x co x 6

r 7 hoose the correct answer below A 14 OE 14 coordinates in three dimensional space OB 146 OC 146 0 OG OD OH

f 7 For the function f x y sin 3x 3y find dx of 7 and f dy

equations for a the tangent plane and b the normal line at the point Po 1 1 0 on the surface x y z 2 Which equation describes the tangent plane OA x y z 2 0 OB x y z 2 0 OC x y z 2 0 OD x y z 2 0 b Select the equations for the normal line OA x 1 t y 1 t z t OC x 1 t y 1 t z t OB x 1 t y 1 t z t OD x 1 t y 1 t z t

Applying these values we get x dx 18 6 1 1 In x9 x18

Given the parametric equations x t 2 and y t 3 4t where 3 t 3 which of the following graphs represents the curve and its orientation 8 7

The Integral Part 2 of 5 To find 1 X18 x dx Vx18 6 TV 6 can be best matched by formula number 43 we can use formula 43 shown below du u a2 In u u a C Using this we have u and a 43 from the Table of Integr

Part 5 of 5 x sin 4x2 cos 9x2 dx 20 Since cos 0 cos 8 then we can rewrite this as C 20 cos 13x 52 52 C