Q2\A telegraph cable is made of an outer winding around an inner core. If x is defined as the core radius divided by the outer radius, the transmission speed is proportional to s(x) = (sin x)sin x. Estimate the value of x that maximizes the transmission speed.

Q: What is the maximum value of y = cos x. For - < x < < ?? 1 1/2 2.

A:

Q: The linear approximation at æ = 0 to sin(2z) is A + Bx where A is:| Previev and where B is: |…

A:

Q: give 3 examples of the reciprocal rule of integration formula

A: The reciprocal rule for the integration is: ∫f'(x)f(x)dx=ln |f(x)|+C

Q: В. Estimate to three decimal places the value of: S V1 + x³ dx by using the trapezium rule with n =…

A:

Q: Find the local linear approximation of f(x) at 4 + x xo = 3, where Ax = x – 3. NOTE: Enter the exact…

A: f(x)=14+x

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

A: Topic = Derivative

Q: sec( c)+y dy e sec do

A: Given differential equation is homogeneous equation

Q: If the acceleration of a particle is given by ä = sint i+ cost +e k, find the relity and position…

A: The acceleration of a particle is…

Q: the metrod of variation of parameters to Apply Solve my = Secnn dx2

A:

Q: A basketball player makes a successful shot from the free throw line. Suppose that the path of the…

A: We have given that in the basketball game ,the ball travels the path given by y=2.15+2.09x-0.41x2…

Q: 3 x dx 1

A: The given integral is ∫13xdx, with total n=4 subintervals. Comparing the given integral with…

Q: The maximum value of y = sin x, 0 &lt;= x &lt;= 2p, isand occurs at x =__________ .

A:

Q: a) Estimate the length of this arc with the length of the line segment joining the endpoints of the…

A:

Q: A stone, projected vertically upward with initial velocity 112 ft/sec, moves according to s = 112t -…

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: Suppose X1, ..., Xn are iid with PDF f (x | 0) = 40ªx-5. x > 0, where 0 > 0. Find the method of…

A:

Q: 3. f Arccos 2xdx

A:

Q: Find the maximum or local minimum f(x)=sinx.[0,4]

A:

Q: Find the maximum rate of change of f (x, y) = xy ^ 2 + root (y) at the point (2,1). in which…

A: The maximum rate of change of f(x, y) happens along the direction grad(f) at the given point (2, 1).…

Q: Find the set of orthogonal trajectories for r = VA sin (2e)

A:

Q: Use Newton's method to approximate the indicated root of f(x)= xª + x – 4 in the interval [1,2]…

A:

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

A: We will find out the required solution.

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

A:

Q: Use differentials to approximate V36.1. 3.

A: Consider y = root x.Let take x = 36 and delta x = 0.1.Find delta y as follows.

Q: Find a double root of the equation f (x) = x' -x -x+1 = 0 by generalized New- ton's method.

A:

Q: A metal storage tank with fixed volume V0 = 360π m^3 is to be constructed in the shape of a right…

A: To find: The dimensions will require the least amount of metal. Given information: A metal storage…

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

A: Given,    no. of tent = 25 ,  average no. of cases=6

Q: 22. Use the Trapezoidal Rule with n = 4 to approximate 1 (x− 1)² dx

A:

Q: What is the isogonal trajectories family of curves x² - y² = a which intersects at an angle of ∅ =…

A:

Q: Does Newton’s Method fail when the initial guess is a relative maximum of f ? Explain.

A:

Q: Obtain the general solution using variation of parameter. (D² + 1)y= cotx

A:

Q: .Find the estimate for the root of f(x) = sin x+ cos (r+1)-1using Bisection methodx, = 1.5, X=2 with…

A: Solution

Q: Find the tangent line approximation for f(x) = v2 – x at x = -2. Use it to estimate the value at x =…

A: Solving using linear approximation formula

Q: .A telegraph cable is made of an outer winding around an inner core. If x is defined as the core…

A: Using double derivative test to get max value of x

Q: What is the value of the function xcosnxdx if we integrate it using Kronecker' smethod?

A:

Q: Find the rate at which the total average number of COVID cases is increasing at x=10 tents and…

A: Let y be the total average COVID cases. Given that at x=10, dxdt=1, where x is the number of tents.…

Q: What values of a and b maximize the value of (x – x²) dx? |(Hint: Where is the integrand positive?)

A:

Q: In integrating the function fx In 5x dx using integration by parts, what would be your v?

A:

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: A particle moves along the x-axis with acceleration given by 5T sin (at) for time t > 0. If the…

A:

Q: 2. Use the Midpoint Rule with n = 4 to estimate (x² + 1) dx %3D

A:

Q: Find the linearization of ƒ(x) = sqrt(1 + x) + sin x - 0.5 at x = 0

A:

Q: Use the trapezium rule, with 4 strips, to estimate fe-a* dx on [0, 2]. What is the maximum error?…

A: Given integration is : ∫02e-x2dx The formula used in trapezium rule is :…

Q: f(x csc² 2x - x cos 2x)dx

A: The given integral is ∫xcsc22x-xcos2xdx. The objective is to solve the given integral. Following…

Q: Use the composite Simpson's rule with step length h=0.5 to determine 1= [ (2x - - 3x2 + 4x – 1)dx,

A:

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…

Q: How large should we take n in order to guarantee that the Trapezoidal Rule approximation for 6 5x*dx…

A:

Q: 1 f(x) = (x² + 3x)² at [2,3]

A:

Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

Linear Functions

A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.