After a new firm starts in business, it finds that its rate of profits (in hundreds c %3D dollars per year) after t years of operation is given by P'(t) = 3t2 + 2t + 11. Find profit in year 5 of the operation. O A) $12,400 B) $19,500 C) $8100 O D) $16,450

Q: Find without using the Chain Rule and the ProductRule

A: We simplify the inner function using the properties of log.

Q: Use Version 1 of the Chain Rule to Calculate dy/dx

A: Given: y=7x-1 We know that ddxxn=nxn-1                                                       ..1

Q: Find the total differential. z = 10x5, y7 dz =

A:

Q: IND THE ORTHOGONAL TRAJECTORIES OF THECURVES Y =Cx²,WHERE CIS AN ARBITRARY CONSTANT.

A:

Q: the linear approximation for f(x,y) = sqrt (y+cos^2 x) at (0,35) is ?

A:

Q: 3 If y= Vx (x-1), find dy (Use rules, not a de finition XP

A: Given:         y=xx-1       dydx=ddxxx-1    Apply product rule:         ux·vx'=u'(x)·v(x)+u(x)·v'(x)…

Q: Show that y" + ay' = b, wherein a and b are constants, can be reduced to y' =+ C₁e-ax using…

A:

Q: tany = C secx

A: The question clearly asks us to find the family of orthogonal trajectories of the given family.…

Q: Transforming A S B © D dx secx + 1 7 dz 1-2² 1==323d² -dz 1+z² [1+2²21 2-272 1+z² -dz -dz using…

A:

Q: Use Euler's method to estimate y(0.02) ey-x y' 1 + e²y ,y(0) = 4

A: Given differential equation is y'=ey-x1+e2y with the initial condition  y0=4 and step size is…

Q: Reverse order, then integrate SaE ) dydx. Vx \1+

A:

Q: Find the orthogonal trajectories of r= a sin? 0 where a be the arbitrary constant.

A: We have, r=a sin2θ .....................................................(1) Differentiating w.r.t.…

Q: Compute dy/dx using the chain rule in formula. State your answer in terms of x only.  y = u3>2, u…

A: Given equations - y = u3+2           .....(1)                                                  In…

Q: Question The approximation of fxln (x + 5) dx using two points Gaussian quadrature formula is:

A:

Q: dz If z = e2x+ 3y and x = In t, y = t2, calculate from the total dt derivative formula and show that…

A:

Q: What is the integrating factor of the linear DE of order one ydx + (3x - 2y +5) dy=0,

A:

Q: Use Picard's method of successive approximation to solve the equation de 1+ xy, y(0) 1 at 8.1 X-0.1.

A: Given differential equation is  dydx=1+xy, y(0) = 1 To approximate the solution at x = 0.1 using…

Q: Find the total differential. z = 2x6y9 dz

A:

Q: 10. The sides of the rectangle at right increase in such a way that the instant when x = 4 and y =…

A: We need to find the value of dxdt, given that dzdt=1,dxdt=3dydt,x=4,y=3

Q: Given: y = sqrt(u)  ,  u = 2x2 + 3x + 4 Determine dy/dx at x = -3 a) Using Leibniz Chain Rule b) By…

A:

Q: Solve using the integrating factors by inspection (y²-3-x) dy + ydx =0

A:

Q: The value of the line integral S(2xy² dx + 2x?ydy + dz) along a path joining the origin and the…

A: To find the value of line integral  ∫c(2xy2dx+2x2ydy+dz)along the path joining origin and point…

Q: In? (In(ax)) dx,a >0 -dr, a a. 2x In(ax)

A: You can solve this problem using the substitution method

Q: Ex. 2. Prove thät if two equal and perfectly elastic balls moving in the same direction collide…

A:

Q: Find work done from the followingW = G- sec²(3x)- V8) dx witch Gx +9 h used to stretch a spring from…

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Q: e ln (xle) (2– sec²r)cm#/c°sec³x sec(3A – x) What should be the value of A for -dx to be integrable…

A:

Q: 1. xy + z2

A:

Q: Find the total differential. z = 5x3y8 dz =

A: The solution is:

Q: Find the total differential. z = 6x1°y8 dz =

A:

Q: Find the quadratic approximation at (0,0) for f(x,y) = ln(1+x^2 + y^2).

A:

Q: Solve the initial-value pxoblem dy dr COSX-Sinx t %3D yro)%3D0 Using Adams. Moulton.

A: Given differential equation is dydx=cosx-sinx+y Let  f(x,y)=cosx-sinx+y                 (1) 0≤x≤0.5,…

Q: A volleyball is moving 16 m/s at 25o North of straight down. If +x is East, +y is North, and +z is…

A: Draw the sketch, as follows: Since the ball is moving 25° North of "Straight Down" direction, its…

Q: Find the total differential. z = 10x4y5 dz = (No Response)

A:

Q: t seel dx

A:

Q: Find the total differential. z = 5x³y4 dz =

A: Solve the given

Q: aw nd dt in term of t, if w = xy, x = cost and y = sint, when t = - %3D

A: Question 4 is not complete.  I am answering Question 5.

Q: The work done W,to stretch a spring from its natural length to an extension of 2 meters Is given by…

A:

Q: a. Apply the Runge-Kutta method of 4th order to find the approximate value of y for x =0.2, dy in…

A:

Q: Find an equation of the tangent llne to the về at the given poln 6x y = (x + 1)2' (0, 0)

A:

Q: Compute dx in two ways and verify that the answers agree.

A: Assume the given integral be I. I can be integrated via trigonometric substitution by substituting…

Q: Show that a particle, located at the origin at t = 1 and moving along the x-axis with velocity v(t)…

A:

Q: Find the total differential. z = 6x *y5 iz

A:

Q: What is the integrating factor of the linear De of order one ydx + (2 – xy)dy= 0 ?

A:

Q: (b)/ Use the Trapezoidal Rule with n = 4 to estimate ſ,(x3 + 1)dx.

A: To find: ∫-11x3 + 1dx using trapezoidal rule with n=4

Q: The rate of vocabulary memorization of the average student in a foreign language course is given by…

A:

Q: Find the differential dy of the given function. Y= square root 7- x^2 Dy=

A: To find the differential dy of the given function

Q: 2s+3 13. F(s) = s2–5

A:

Q: If you have the equation dx/dt = a,are you allowed to multiply both sides by dt to change the…

A: We have given,

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.