Differential equations Questions and Answers
Calculus
Differential equationsT 13 Exponential growth and decay word problems TYQ A colony of 100 bacteria doubles in size every 60 hours What will the population be 180 hours from now
Calculus
Differential equationsThe graph of y f x is shown in blue Draw the graph of y f x shown in red by determining how a stretch or compression will transform the location of the indicated blue points Drag the movable red points to the desired coordinates You may click on a point to verify its coordinates
Calculus
Differential equationsind a formula for the linear function depicted in the following graph Answer 10 ta Av Hop S Enable Zoom Pan X
Calculus
Differential equations3 Consider the finite difference formula 1 f x f x 2h 8f x h 8f x h f x 2h 0 h 12h Derive this formula by using Taylor s theorem Hint set n 4 in Taylor s expan sion
Calculus
Differential equationsWhich of the following matrices is in reduced row echelon form Select one O a O b O C O d 105 0 5 0 0 1 10 1 0 1 00 0 0 0 1 1 2 0 0 00 1 0 00 0001 0 0 0 05 07
Calculus
Differential equationsSolve the given initial value problem for y f x dy 1 y where y 6 when x 2 2 x 1 4 O y ln x 1 6 O y ln x 1 6 O y In d 1 6 4
Calculus
Differential equationsSolve the given initial value problem for y f x dy e4 x where y 0 when x 4 y x 4 4e4 x y x 1 e4 x y x 4 4e4 x y x 1 e4 X
Calculus
Differential equationse initial height Question 2 A soccer ball is kicked across a field Determine how long the soccer ball
Calculus
Differential equations8 For the tangent line to the curve at the origin for r 2sin20 a 0 0 0 37 c 8 0 2 b d 0 0 0 0 0 0 EINE
Calculus
Differential equations5 Find the equation for the ellipse with foci 11 0 and semimajor axis a 6 a 25 y 1 36 c 2 1 36 25 b d 6 5 5 1 1 y 1 6
Calculus
Differential equationsFind the function p that satisfies the following conditions assume x 0 30 231 p x p 4 8
Calculus
Differential equationsA particle moves on a straight line and has acceleration a t 36t 6 Its position at time t 0 is s 0 10 and its velocity at time t 0 is v 0 3 What is its position at time t 6
Calculus
Differential equationsGiven f x then f x f x Note that your answer should not contain a general constant e with f 0 9 f 0 5 C
Calculus
Differential equationsUsing known series determine the Taylor series for the function f x 1 1 x 2 x In 2 x x sin2 x at x 0
Calculus
Differential equationsProcedure For the differential equation y y 6y 0 y and y2 y lead to the system the substitutions y y y2 y 6y y2 Use the procedure to solve y y 42y 0 NOTE Use c and ce for the constants of integration Y1
Calculus
Differential equations15 If f x 3 9x x which of the following is true about the end behavior of f x As z f z and as z f x As I f x and as a f x 0 As I f 1 and as a f x As I f x and as o f x None of the above
Calculus
Differential equationsFind the difference of the complex numbers in the complex plane 4 3 31
Calculus
Differential equationsFind the missing values by solving the parallelogram shown in the figure The lengths of the diagonals are given by c and d Round your answers to two decimal places C 3 01 X a 5 b 6 a 0 b d 10 63 x 0 30 150 0
Calculus
Differential equationsnge in the radius during that time 230 A spherical balloon is being inflated at a constant rate If the volume of the balloon changes from 36 in 3 to 2887 in between time t 30 and t 60 seconds find the net change in the radius of the balloon during that time
Calculus
Differential equationsA company finds that the rate at which the quantity of a product that consumers demand changes with respect to price is given by the marginal demand function D x 5000 where x is the price per unit in dollars Find the demand function if it is known that 1004 units of the product are demanded by consumers when the price is 5 per unit Dod
Calculus
Differential equationsDetermine whether there is a relative maximum a relative minimum a saddle point or insufficient information to determine the nature of the function f x y at the critical point xo Yo fxx xor Yo 25 fyy xor Yo 7 fxy xo Yo 10 relative minimum insufficient information O saddle point relative maximum
Calculus
Differential equationsThe following sum is a right Riemann sum for the definite integral where b and f x 2 40 7 49 n The limit of these Riom 2 7n 49 44 2 40 TH 7 12 77 n n n f x f x dx
Calculus
Differential equationsConsider the integral L 2 dz a Find the Riemann sum for this integral using right endpoints and n 4 b Find the Riemann sum for this same integral using left endpoints and n 4
Calculus
Differential equationsDetermine a function that satisfies the differential equation d y dx2 4y b Explain how you found your CO
Calculus
Differential equationsIntegrate assuming x 0 S xin x In 5x dx x n Type an exact answer x In 5x dx
Calculus
Differential equationsthe recurrence relation for the power series solution about x 0 of the differential equation y y 0 is
Calculus
Differential equations6 Find at least first four non zero terms with the help of recurrence relation of two linearly independent solutions in a power series expansion about r 0 for a general solution to the given differential equation
Calculus
Differential equationsFor each of the following part make sure to show and justify your steps dy a Find the general solution to the equation dx b Find the solution which goes though the point 2 4 4y 12 c Does this equation have any equilibrium solutions If so find them and classify as stal or unstable
Calculus
Differential equationsFind polar equations of the tangent lines to the curve at the pole r 2cos 30
Calculus
Differential equationsThe price per barrel of crude oil in the period 1980 2013 in constant 2014 dollars can be approximated by P t 0 27t 8 6t 93 dollars 0 t 33 where t is time in years since the start of 1980 Find P t and P 31 P t P 31 per year What does the second answer tell you about the price of crude oil Hint See Example 2 The price of a barrel of crude oil was increasing at a rate of per year in
Calculus
Differential equationsIn Problems 1 8 state the order of the given ordinary differ ential equation Determine whether the equation is linear or nonlinear by matching it with 6 Le 1 1 x y 4xy 5y cos x dy y 0 dx 1 6y 0 du dr 2 x 3 15y 4 d u dr 4 dx 5 dx u cos r u 1 dy dx
Calculus
Differential equationsThe region in the first quadrant bounded by y 4x 3x y 7 and the y axis is rotate about the line x 3
Calculus
Differential equationsExpone Sometimes we don t need to model rapid growth but rather rather decline We can use the exponential decay model P t Pe kt where k is the exponential decay rate k 0 Pis the initial amount and t is the time otore that calls 85 000 each
Calculus
Differential equationsA woman invests 6200 in an account that pays 6 interest per year compounded continuously a What is the amount after 2 years Round your answer to the nearest cent b How long will it take for the amount to be 8000 Round your answer to two decimal places yr
Calculus
Differential equationsSketch a graph of a function f that has at least all of the following properties Draw in any vertical asymptote s where appropriate lim x 6 f x 4 lim x 3 f x 18 f 0 2 f x 0 when x 2 f0 5 0 lim x 8 f x 1 lim x 8 f x 4 limx f x
Calculus
Differential equationsFind the linear approximation of the function f x 1 x at a 0 L x Use L x to approximate the numbers 0 9 and 0 99 Round your answers to four decimal places 0 9 0 99 Illustrate by graphing f and the tangent line y 2 1 2 1 2 3 1 2 3 4 WebAssign Plot 5 X 5 2 5 10 15 20
Calculus
Differential equationsaluate the integral by making an appropriate change of variables 7 Cos 5 YX dA where R is the trapezoidal region with vertices 1 0 8 0 0 8 and
Calculus
Differential equations4 Use geometry or symmetry or both to evaluate the integral 2 2 y y sin z dA where D x y x y 1