Calculus Questions

Let A x represent the area bounded by the graph the horizontal axis and the vertical lines at t 0 and t x for the graph below Evaluate A x for x 1 2 3 and 4 5 4 3 2 1 A 1 A 2 A 3 A 4 2 Question Help Video Add Work 3 4 5

The velocity of a car is f t 10t meters per second Use a graph of f t to find the exact distance travelled by the car in meters from t 0 to t 8 seconds Distance m

An airplane is traveling in the direction 30 west of north at 700 km hr Find the component form of the velocity of the airplane assuming that the positive x axis represents due east and the positive y axis represents due north What is the component form of the velocity of the airplane Round the final answer to one decimal place as needed

If AB i 7j 2k and B is the point 7 5 6 find A The point A is

If f x determine the antiderivative of f x Do not include the constant Cin 8 x 4 your answer Note When entering natural log in your answer enter lowercase LN as In There is no natural log button on the Alta keyboard

6a 4a 6 da Do not include the constant C in your answer For example if you found the antiderivative was 2x C you would enter 2 What is

Find the particular solution to the differential equation below such that y 0 8 y 6e 6x 9x Do not include y in your answer

1 8 Evaluate the integral by making the given substitution 1 fcos 2x dx u 2x xe x dx u x 3 fx x 1dx u x 1 2

1 8 Evaluate the integral by making the given substitution 1 cos 2x dx u 2x 2 fxe x dx u x 2

Find the anti derivative of g x x x Do not include the constant C in your answer

3 2 f x x 4x 4x

d 1 20 x 3 4x dx 20 5 0 do f 3R R 5R dR

3 2 f x x 4x 4x Find all real numbers a so that the function dy continious at a X

Let u 7 4 and v 5 3 Find the a component form and b magnitude length of the vector 8 15 u 17u 17 v 8 15 17 17 Tyne integers a VE simplified fractions

3 y x 3x 5 Find an equation of all the horizontal tan

5

5 9 X 0

lim X sin x X COS X X

Consider the system of linear equation 11 p 11 2 9 a Find a particular solution for the given system of linear equation h 6 5 15 2 1 1 3 9 5 5 14 6 1 4 b Find a non trivial homogeneous solution for the given system of linear equation

lim X 1 5 4 3 x 3x 2x 1 1 X 1

second derivative of the functions Wiritize in the variannes a y 2 74 44 5 1 S xy y x 0

1 8 Evaluate the integral by making the given substitution 1 cos 2x dx u 2x

2 3 Write an equation for a rational function with Vertical asymptotes at x 4 and x 2 x intercepts at x 6 and x 5 y intercept at 9 y Write an equation for a rational function with Vertical asymptotes at x 4 and x 2 x intercepts at x 1 and x 1 Horizontal asymptote at y 7 y Write an equation for the function graphed below 7 6 5

Write the equation for the graph below 40 y 3 7 6 Write an equation for the function graphed below 4 3 3 20 4 34 2 2 3 6 7 2 Write the equation for the graph below 10 y 10 9

1 Evaluate the integral 4x y z dxdydz

es e O Rama produces two bike models Voltage and EasyRider Departmental overhead data follow Department Fabricating Assembly Budgeted Cost 97 200 80 000 Allocation Base Machine hours MH Direct labor hours DLH Required 1 Compute departmental overhead rates using a machine hours to allocate budgeted Fabricating costs and b direct labor hours to allocate budgeted Assembly costs 2 The company reports the following actual production usage data Compute the overhead cost per unit for each model Machine hours per unit Voltage 2 0 MH 1 6 DLH Direct labor hours per unit 3 The company reports additional information below For each model compute the product cost per unit Direct Materials Budgeted Usage 8 100 MH 1 600 DLH EasyRider 3 0 MH 0 5 DLH 91 81 Per Unit Selling Price Voltage EasyRider 261 151 4 For each model compute gross profit per unit selling price per unit minus product cost per unit Direct Labor 46 16 Complete this question by entering your answers in the tabs below

The pie chart to the right shows how adults rate their financial shape Suppose 18 people are chosen at random from a group of 500 What is the probability that none of the 18 people would rate their financial shape as fair Make the assumption that the 500 people are represented by the pie chart The probability that none of the 18 people would rate their financial shape as fair is Round to six decimal places as needed Excellent 4 Good 42 Fair 38 Poor 14 Other 2

1 Nyx is in the middle of a crafts project For this portion of their project they are designing stylized bird feathers They construct the feathers in the following way First they glue two concentric circles made of construction paper together a 10 diameter one made of white paper placed on top of a 12 5 diameter one made of black paper Next they cut the circles into twelve equal wedges I 12 5 10 Nyx wants to finish the feathers by adding a strip of tinsel along the border of the dark region of each feather How much tinsel will they need for one feather Write your answer below Show all work including any assumptions you make

Question 6 24x 57x 3x 6 Find the equation of the vertical asymptote and the equation of the slant asymptote of the rational function f x 1 Question Help 5 23 The equation of the vertical asymptote is x The equation of the slant asymptote is y

Find the equation of the slant asymptote of the rational function 2x 10x2 7x 24 f x 2x 5 The equation of the slant asymptote is y

Find the horizontal asymptote of f x y 4x 3x 5 5c3 c2 3

roblem 5 a Suppose that f x x 3 x b Suppose that f x 6 1 x for x 0 and that 1 1 Find 4 and that f 0 5 Find 3

The distribution of IQ scores is often modeled by the normal distribution with mean 100 and standard deviation 15 a Write a formula for the density distribution of IQ scores 1 15 2 T p x x 100 450 07 e b Estimate the fraction of the population with IQ between 114 and 119 NOTE Round your answers to one decimal place

I Find dz where C is the line segment from 2 i to i af z fon

Find the arc length parameter along the curve from the point where t 0 by evaluating the integral s v T dt T 0 Then find the length of the indicated portion of the curve r t 8 4t i 3 7t j 9 2t k 1st 0 The arc length parameter is s t Type an exact answer using radicals as needed

Find the median of the density function given by p t Round your answer to one decimal place The median is Toxtbook and Media 0 04 0 0008t for 0 t 50 using the Fundamental Theorem of Calculus

Evaluate the following integral 2 sipx IIT siny dz dx dy 000 x 2 sipx siny dz dx dy 00 0 Simplify your answer Type an exact answer using as needed Use integers or fractions for any nu the expression

10 Given y f x CSC cot 1n 9x find dy dx

Evaluate the following integral 341 N LEX x y dz dx dy dz dx dy Simplify your answer www

A E Match each of the following graphs with the correct function by placing the letter of the graph on the line provided Each letter can only be used once Do not use a calculator or desmos to draw the graph 3 f x x 1 2 4 f x x 1 1 0 5 f x x 2x 1 6 f x x 2x 1 7 f x x 8 f x x 2x 9 f x x 2x 3 10 f x x 2x 2 2x 2 3 2 0 1 B F 1 1 2 2 1 0 2 0 1 2 2 1 1 3 x D V 2 3 1 1 1

Use Newton s method to approximate all the intersection points of the following pair of curves Some preliminary graphing or analysis may help choosing good initial approximations y 4 sin x and y 9x 7

Solve the following initial value probl 3 g 7x 47 12 g 1 24 B h A 1 6 sont h 35 3

Find the following indefinite integrals 142 98 2101 dy 7 4 2 Sseek Seco tan Seed cose d

Solve the following initial value problems 2x fla 4 200d sil f 1 0 x x 4 4 1 0 0 f x xex

Find the following indefinite integrals astias 4 2 X X 4X 5 X 14 dx df et

ind the absolute maximum and minimum of f x y 3x 3y within the domain x y 4 1 Absolute minimum of f x y is 2 Absolute maximum of f x y is 4 64 4 64 X 8 4852813742386 x 8 4852813742386

Suppose 30 of the people in your town talk on their cell phones and drive at the same time If you stood on a busy street corner and watched 50 people drive by about what proportion would you expect to see talking on their cell phones Choose the correct answer below OA 0 30 OB 50 O C 15 OD Not enough information is given to answer the question Submit quiz CLOS

Find the most general antiderivative of f x F x tvt vt 2t

2 The parent function broken line is y f x Describe the exact transformations to its image then write the coordinate rule Write the equation of its image in function form Description Coordinate Rule Parent y f x Image g x 7 6 5 A 34 2 1 2 3 y 2 3 16

tan 15x 4 1 0 4 810 5N Alm 4x 3 O 0 1 0 1 W SPE 4 19 1 0 4 Type an exact answer usin