a) Show that if y = V1 + sin x then =: %3D b) A manufacturer estimates that x units of a particular commodity will be sold when the price is p(x): = 112 – xlnx3 hundred dollars per unit. What is the marginal revenue associated with the nommodity when 4 units are sold? will be increasing at the

Q: Assumee thát ic COst C(x) = 25,600 + 100x + 0.01x² dollars to manufacture x 32GB iPods in a day. t…

A: given cost functio cx=25600+100x=0.1x2

Q: Q2 find the derivative of the following: 1) y = 2stn²(5x) ,2) y = Inx'n cosh 5x ,3) xsin¬14y = y…

A:

Q: 5. Find of the parameters: x = sin 2t and y = - cost at t = dx %3D

A: Topic = Derivative

Q: 1- Find the equation of the tangent to the curve y = 2 sin x+ cos2x at the point x = n. 2- Find the…

A: Solution:

Q: Find the general solution using reduction of order. 1. y''=ln(x)

A:

Q: 1. Ye = cost- sec(at) %3D ans: =-2sin t - asec(at) tan(at)

A:

Q: 2. The rate at which the total average of COVID cases is dx increasing at x = 10 tents and 1 tent…

A: The solution are next step

Q: Find the partial derivative of the given In[y? sec(x²y²)].

A:

Q: Use Euler's Method with an appropriate h value of your choosing to estimate y(4) with y = 0.5, y (1)…

A: Topic- Differential Equation

Q: 1. Compute forward approximations of O(h) and O(h² for the first derivative of y = e* evaluated at x…

A: 1st we will derive formula for O(h) and O(h2) and then find corresponding values

Q: Find the derivative of the function. rcos(x) y = In(1+2t)dt sin(x)

A: Applying Leibniz rule

Q: 2. The rate at which the total average of COVID cases is dz increasing at r = 10 tents and than if…

A: If 30 tents are built, the average number of COVID cases per tent will be 7 cases while the average…

Q: Given a right circular cone with an altitude of 5 cm and a base diameter of 8 cm. If the diameter is…

A: volume of cone =Πr2h/3

Q: A 20 kg wagon moving at a speed of 0.5 m/s towards right collides with a 35 kg wagon which is at…

A: Solution:

Q: Assume that it costs a company approximately C(x) = 529,000 + 160x + 0.001x2 dollars to manufacture…

A:

Q: y = (Arccos 3x³)³

A:

Q: TOL Company Ltd have undertaken an investigation for a client cor and has discovered that the total…

A:

Q: Show that Costy+ Co5' (-x ) = TT.

A: To show that the given identity is true,

Q: Determine the first derivative of the ff. function a. y = 400(2)**3 sin 3x b. y = Vxe2* cos x…

A:

Q: Can you help me with this problem step by step?

A: The given equation,

Q: find x which minimizes the following function and its minimum with differentiation technique.…

A: We will find out the required solution.

Q: 2 1 Estimate -dx using the right endpoint rule with n = 4 3 1+x

A:

Q: If tan2(2y) – S cost dt = 4 - x² %3D dx

A:

Q: Apply variation of parameters to find a particular solution of y ''' - y' = tan x

A: The given differential equation is y''-y' = tan x.We have to solve this using the variation of…

Q: 5. Find the derivative of y = In(cos v3x + 2 ), by using chain Rule.

A:

Q: the derivative of y with respect to v. 1 = In ( cosh (5v)) –· tanh 2(5v) 2 derivative of y with…

A:

Q: 11. Find the length of the curve x = on the interval (2, 4] (integrate with respect to y) 12y3 un

A: Given that the function x =y55+112y3 Find the arc length of the graph of the given curve on the…

Q: 1 log3(r – y)*

A: Given; fx,y=1log3x-y   As we know that; The Power law: ddxxn=nxn-1 The Chain rule: fgx'=f'gx·g'x And…

Q: The GoldPlus Company determines that the marginal cost for their Aiibe 64GB flash drive is given by…

A: One of the methods to solve a differential equation is by separating the variables and integrating…

Q: 2. The radius and height of a right-circular cylinder are measured with errors at most 0.1 inches.…

A:

Q: 1- Solve the second derivative forf(x, y,z) = e sinay3) əx2

A:

Q: 22. Find the derivative of y = arcos(4x) with respect to x. - 4 4 - 4 - 4 В. 1-4x2 С. Vi-(4x) A. D.…

A:

Q: Suppose that a drug is administered to a person in a single dose, and assume that the drug does not…

A:

Q: (b) Use implicit differentiation by partial derivative to solve for dx of the function 5x + xy 4y.

A:

Q: The derivative of y= sech-1(x sechx)+e$inh (Inx) equals Select one: – x sechx tanhx+ sechx O y:…

A: Given

Q: 2. Approximate the derivative of f(x) forward, backward, and central difference method and step size…

A: To obtain the derivative at the point x0,y0, the following methods can be used:- The forward…

Q: Use Richardson extrapolation to estimate the first derivative of Y = sin x at * = π/4 using step…

A: Given the function  y=sinx

Q: 5. Consider the function f(x)=e*, calculate df/dx with finite difference using forward and central…

A: We can solve this using formula of central difference and

Q: The derivative of y= sech1(Inx)+esinh(3x) equals Select one: 1 3e sinh"(3x) O y' = - xInx/1-Inx…

A: Proceed as shown below...

Q: Find2 of the parameters: x = sin 2t and y = - cost at t =

A: In this question, we need to find dydx. It is given that x = sin 2t and y = -cos t

Q: (g) y = Vtanh 3r (h) y= sinh(cosh 2.x)

A:

Q: 1 By considering the secant through the points where x = 1.2 and x = instantaneous rate of change of…

A:

Q: If fex, yJ-o find dy /af partial derivative off dx

A:

Q: A total cost function (in dollars) is given by C(x) = 116 + 3x + 0.37x. Use differentials to…

A:

Q: what is the maximum value of y=sinx, 0 less than or equal to x less than or equal to 2pie, and…

A: Given function  y = sinx on  0≤x≤2π

Q: 16. What is the derivative of the function: * y = sin(6x² - 1) y = 12x cos(6x² - 1) y' = x cos(6x² -…

A: Solving the problem by finding the value of the derivative.

Q: If the first derivative of y is -3.8025 sin(0.507 t) on the interval {0 <= t <= 24}, what are the…

A:

Q: 9. Consider the interval [0, 2n] for the function y sec x. State an x- value at which the…

A: Given query is to find value of x for different conditions for instantaneous rate of change.

Q: 2. Find two positive numbers whose product is 750 and for which the sum of one and 10 times the…

A: Product of two numbers:= 750; Sum of one and 10times the other is minimum;

Q: The minimum value of n required to approximate xe dx by composite Trapezoidal rule with an error…

A: Find the minimum value of n required to approximate ∫02xe-xdx by composite Trapezoidal rule with and…