Application of derivatives Questions and Answers

D Choose the correct answe OA 10 km OB 10 cm2 O c 10 m

A sector of area 37 2 square inches is formed by a central angle of 30 What is the radius of the circle Round your answer to two decimal places

Sive the order of the differential equation below where y represents a function of the variable x

Conversions to and fro Metric System The speed limit is 40 kilomete per hour

Solve the following initial value problem a y 3x y y 0 dy dx b dy dx 4 5 y 0 2 x3 Note Your explanation should include all the calculus and algebra steps that are of solving each initial value problem Your final answer should be written in the on the left with a function of x on the right

D The following scorecard shows of a golf course Determine the Hole 1 23 4 Black Blue Tees Tees 507 507 187 177 365 356 392 372 Handicap 3 15 11 7

1 For each differential equations below state whether the differential equation is separa ble or not If separable make sure to write it in a separable form that is g y h x Clearly justify your answers and show your work a b C d dy dx dy dx da dy da xe y 1 y 4x y y 3x y y 5 x3

1 Recall the E U Theorem for linear homogeneous ODEs a Let 6 if t 0 5 ift 0 if t 0 if t 0 on Find the general solution for the equation y p t q t y 0 p t be a tB 0 What is the dimension of the solution space Why it doesn t contradict the uniqueness of solutions for second order linear equations b Let A t and 9 t 3 x 3 matrix of coefficients continuous on 1 2 9 6 4 5 Consider the linear ODE x A t x What is the dimension of solutions on

Convert the quantity to the indica 20 6 L to pints pints Round to th

An object with initial temperature 200 F is submerged in large tank of water whose temperature is 40 F Find a formula for F t the temperature of the object after t minutes if the cooling constant is k 0 2 F t 150 0 2t 40 X

Sketch the graph of Y x 1 and find the area enclosed by this curve x 3 x 1and x axis

5 Let f x 2 ln x 5 a Apply inverse functions to solve for the input s x that results in the output f x 4

Graph the following piecewise function determine its range and evaluate f 3 4x 4 0 f x 3x 2 TVO Clear All Draw Hint 10 9 8 The range of fis 6 5 4 327 10 9 8 7 6 5 4 3 2 1 1 3 2 1234 5 6 7 8 9 0 2 3 4 5 6 7 8 9 10 1 2 3 4 5 6 7 8 9 10

Solve the following initial value problem y 1 7y1 y2 y 2 6y1 2y2 y1 0 4 y2 0 3 Enter the functions y1 x and y2 x in that order into the answer box below separated with a comma Do not include y1 x or y2 x in your answer

The transfer function for a linear time invariant control system is given as 1 s 1 88 3 H s Show that 1 10 4s 3 S 2 3 1s 11 3 3 1s 11 3 H s 1 1

oblem 3 1 point h x tan cos5 x compose h x into two functio

a Find the average value of f on the given interval b Find c in the given interval such that fave f c c Sketch the graph of f and a rectangle whose base is the given interval and whose area is the same as the area under the graph of f 4 9 f t 1 1 3 10 g x x 1 0 2 11 f x 2 sin r sin 2 r 10 T

oblem 5 1 point et h x cos x5 8 ecompose h into two functio

f x x 1 g x 2x 1 f Find 8 and state the domain O 5x 1 2x 1 O 5x 1 2x 1 O 2x 1 5x 1 O 2r 1 5x 1 Domain x Domain x Domain x Domain x 2 1 5 1 2 1 5

O O 1 1 2 2 0 2x 1 2 O 2x12 O 1 1 2 2 QUESTION 19 Find the derivative 1 1 1 1 x h 1 x h 1 X x

f x 3x find the equation of the tangent line at the point 1 3 y 6x 3 Oy x 3 Oy 6x 3 Oy x 3

x 4 lim x 2x 2 O Does not exist O 0 01 0 2

8 4 turkey sandwiches and 7 french fries cost 17 70 5 turkey sandwiches and 5 french fries cos 18 Find the cost for 1 turkey sandwich and 1 french fries

A B C Click on a graph to enlarge it Graphs The graph of y ln x is graph The graph of y e is graph Inverses D The inverse of y In x is the function y The inverse of y e is the function y E LL Domains Enter an interval in the form a b a b a b or a b Write infinity for and infinity for co Click here for more help on entering intervals The domain of y ln x is the interval The domain of y e is the interval F

Jump to Problem 1 2 3 4 5 6 7 8 9 Problem 1 1 point If there is more than one answer separate If the answer is an interval enter it in the f for and infinity for Click here for r Let f x be the polynomial x x

5m A particle moves along the x axis with velocity given by v t 18 sin 6t for time t 0 If the particle is at position a 3 at time t what is the position of th particle at time t 36

Mar 10 681 PM Given selected value of the function and its derivative in the table below determin the value of lim 5 5m 12 20 200 in simplest form 1 2 w 0 6 3 9 1 9 HAR 4 10 7 1

Preview My An Your score was re You have attempt

Pallabi Sekhar Associates a partnership firm made these transactions Find out the effect on Assets Liabilitie and Capital of the Firm in an Accounting Equation form 1 Business started with 75 000 as capital introduced 2 Taken a Loan from Rajesh and Purchased a computer worth 3 750 3 Additional Capital Invested 15 320 in the form of Equipment 4 Paid Rent in advance 22 500 by cash only 5 Bought a Generator of value 25 000 from Harish Ltd by taking loan from Rajesh again Withdrawn an amount of 10 500 by the Partner for personal purposes Deposited into Firm s Bank an amount of 25 000

1 2 x 4 x 1 2 2x y 1 y 1 2 x 1 the slope of each segment e of bar AB e of bar AD e of bar DC e of bar BC lain why ABCD is a parallelogram

9 Given f x x 2x 3 a Compute the first derivative Make a sign chart as demonstrated in lecture to indicate the intervals of increase and decrease Find any local maximum and minimum values b Compute the second derivative Make a sign chart as demonstrated in lecture to indicate the intervals of concavity Find any inflection points c Sketch a neat and accurate graph You may find this fact useful 0 6

Use the closed interval method to find the absolute maximum and absolute minimum values of f x 12 4x x on 0 5

2 At x 3 the tangent line to the graph of a function f x is y 4x 5 What is f 3 How do you know

6x 2 15x 9

76 Use Simpson s Rule with n 6 to estimate the area under the curve y e x from x 1 to x 4

72 For what values of a is fo the integral for those values cos x dx convergent Evaluate of a ear

Question 21 Multiple Choice Worth 1 points Federal Income Taxes and Piecewise Functions MC The graph of a piecewise function is shown 7 9 19 L 0 00 00 7 0 00 00 NO O 2 u 1 00 B O 2 u 1 00 5 3 2 d L 2 What is the range of the function 6 5 4 T 2 3 4 5 6

nitial Knowledge Check ose that the relation T is defined as T 2 6 7 9 7 2 the domain and range of T e your answers using set notation

1 Use the equation y x 9 to answer part Select the correct choice below and if neces complete your choice The x intercept s is are 3 0 3 0 Use a comma to separate answers ordered pair

Ex Write the equation for the horizo 6x 3x 2 2x 5x 8 f x f x 6x5 2x 1 5x 3x 8

du Find the function u u t given that u 0 0 and dt Answer u t 5te3u

The radius of a circle is 12 centimeters What is the length of an arc that subtends an angle of radians 8

he half life of Radium 226 is 1590 years If a sample contains 400 mg how many mg will remain fter 1000 years 240 02 x mg Sive your answer accurate to at least 2 decimal places

2 Find the quotient and remainder of 8x 6x 3x 1 2x x 2

1 point Sketch the region enclosed by the curves and find its area y e y e x x 0 x ln 3 AREA 0

A rotating light is located 11 feet from a wall The light completes one rotation every 5 seconds Find the rate at which the light projected onto the wall is moving along the wall when the light s angle is 10 degrees from perpendicular to the wall light wall Q feet per second

Gravel is being dumped from a conveyor belt at a rate of 30 cubic feet per minute It forms a pile in the shape of a right circular cone whose base diameter and height are always equal How fast is the height of the pile increasing when the pile is 23 feet high Recall that the volume of a right circular cone with height h and radius of the base r is given by 1 r h 3 V ft

2 At x 2 the tangent line to the graph of a function f x is y 3x 7 What is f 2 How do you know

Solve each equation for exact solutions over the interval 0 2m S 13 2 cos 2x 1 11 3 tan 3x 3

A plane is flying at a constant altitude The angle of depression from the center of the plane to the base of a control tower is 32 After the plane flies 5 miles toward the control tower the angle of depression is 40 At what altitude is the plane flying 5 miles 40 Round your answer to 2 decimal places 328 E Not drawn to scale