For the IVP v' = 1+. 1sts2 h= 0.5 (1) = 2 Find y(1.5) using Runge-Kutta of order 4 Select one: а. 1.6078 Б. 3.5244 c. 1.7067 d. 3.6078

Q: The linearization of ex at x = 1 Estimate to five decimal places the magnitude of the error involved…

A:

Q: Find the maxamin s in flectlon Points and the in ter Vals on which the function inerease,decrease…

A: follow the solution which is mentioned in step 2.

Q: If x2 + y2 = 100 and dy/dt = 8, find dx/dt when y = 6. (Enter your answers as a comma-separated…

A: Consider the given: x2+y2=100 Differentiate w.r.t. "t",…

Q: Let y = V7-T. Find the differential dy when r = 4 and dr 0.2 Find the differential dy when r = 4 and…

A:

Q: find a general sulution to the differential eguatiun using variation of A parametert b)yィyニ tantee…

A: Method of Variation of Parameters: This method is quite general and applies to equations of the form…

Q: Q1/ Evaluate So (x² + 3y²) dy dx using Simpson's 1/3 rule in x-axis and Simpson's 3/8 rule in y axis

A: 1 Given integral is ∫03∫01x2+3y2dydx. We have to evaluate the given integral  by using Simpson's 13…

Q: Assume that after few w months, butterf lies papulace in looa is Calculated as: F(w)=12W+Cos (lbw)…

A: Minimum and maximum of a function can be calculated by testing the function against all the values…

Q: 0. dy for y = 4t dt. 4t +1 3x3 Use Leibniz's rule to find хр

A:

Q: With α = .05 and df = 8, the critical values for a two-tailed t-test are t = ±2.306.  Assuming all…

A:

Q: Use the RK4 method with h = 0.1 to obtain a four-decimal approximation of the indicated value.…

A:

Q: A cylinder of radius r and height h has volume V = nr 2h.(a) Use the Linear Approximation to show…

A: Given: A cylinder of radius r and height h has volume V=πr2h a)  show:  ΔVV≈2Δrr+Δhhb)  Percentage…

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

A:

Q: Use the RK4 method with h = 0.1 to obtain a four-decimal approximation to the indicated value.…

A:

Q: Find dydx? for f(x, y) = eXy

A:

Q: Use the RK4 method with h = 0.1 to obtain a four-decimal approximation of the indicated value.…

A:

Q: 4. 2a y' = y (y² + 3x?)

A: For the solution follow the next steps.

Q: 4. Suppose that z = x³y, x= t², and y = t³, find . dt = 12t11 dt 11t10 b) = 10t° dt d) = 9t® dt

A: This question is related to differentiation, We will solve it using given information.

Q: dy dt 1. y=V(3t2 - 2t + 1)(t2 – 1), 12/07/2021 18: 54

A: Given that       y = √(3t2-2t+1)(t2-1)  Here we have to find dy/dt .

Q: b) Calculate dx for n = 6, using Trapezoidal rule. 1+x5

A: Trapezoidal rule:   where

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

A:

Q: Q5. If W = x² y + 2xyz , x = t², y = t + 1, z = 2t at t = 1. Find the total differential

A: Let's find.

Q: Find the total differential z = 1/2 (ex2+y2− e−x2−y2)

A: The given function is z=12ex2+y2-e-x2-y2. Note that  ∂z∂x=12ex2+y22x-e-x2-y2-2x=xex2+y2-e-x2-y2…

Q: O y²dx + Cory ty² -Ddy

A: Given y2dx+(3xy-y2-1)dy=0

Q: Use the RK4 method with h = 0.1 to obtain a four-decimal approximation to th indicated value. y' =…

A:

Q: Find dy/dr by differentiating implicitly if z +ry- 6r = 2.

A:

Q: Find the length of the curve y = V cos 2t dt from x= 0 to x = 4

A:

Q: Use RK2 (Heun's method) with ħ = 0.5 to estimate y(1) given o: 8 Vū, y(t = 0) = 8, y' (t = 0) = 2.…

A: The Heun's method formula is The given values are h=0.5, y(0)=8, y'(0)=2 That is x0=0,y0=8 and…

Q: As a special case in which the error of Euler's method can be analyzed directly, consider Euler's…

A: Given,   Y'(t)=y(t),   Y(0)=1

Q: Vēt VE dt

A: Our Aim is to evaluate the integral given below:-

Q: Classify the y'+y enx=0 dlifferantial equeltion dnd Pind its generdl solvtion.

A:

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

A: The solution is:

Q: Find the total differential. 4x + y w = 2z - 8y |

A:

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

A:

Q: - By using integration by parts method, calculate the following (choose TWO only) 1- , 2x e* dx 2-…

A:

Q: Compute Y (II) withe y" y'= -8 (Sinx+cosx. Y(T) = 0, y¹ (F) --8, by @ Taylor Series

A: Given differential equation is y''-y'=-8(sinx+cosx)     (1) and y(π)=0, y'(π)=-8 Solution a: Using…

Q: Q3) Compute for y(x) = csc3(4x) + 2x – 3 and x(t) = 4sin t² at t=1 dt %3D

A: Let y(x)=csc3(4x)+2x-3 and x(t)=4sint2 Differentiate y(x) with respect to x…

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 general selution of the differential equetion by the fimear methodi sxy'-2y=x

A:

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

A: Solve the given

Q: Q3/ Evaluate 2 vsinx dx, using i- Trapezoidal rule ii- Simpson's 3/8 rule Ans. 1.1615

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: Let y'=sinxy and y(0)=2 Approximate y(4) using Euler's method with step sizes of .25

A: The solution of a differential equation is defined as the function that satisfies the differential…

Q: sech 2t dt Evaluate 3, coth 2t

A:

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

A:

Q: 2. Reverse the order of integration of S Saz dxdy. y+2

A: The objective is to reverse the order of integration

Q: Q3/ Evaluate Sz Vsinx dx, using i- Trapezoidal rule ii- Simpson's 3/8 rule Ans. 1.1615

A: 3 Given integral is ∫0π2sinxdx. i We have to evaluate the given integral by using trapezoidal rule.…

Q: (b) If z = 9t²e 4t, find 4 dz dt

A: Given.

Q: التاريخ H.w: Campute y fas) With -xýet-x)e | Find @ Euler pc

A:

Riemann Sum

Riemann Sums is a special type of approximation of the area under a curve by dividing it into multiple simple shapes like rectangles or trapezoids and is used in integrals when finite sums are involved. Figuring out the area of a curve is complex hence this method makes it simple. Usually, we take the help of different integration methods for this purpose. This is one of the major parts of integral calculus. 

Riemann Integral

Bernhard Riemann's integral was the first systematic description of the integral of a function on an interval in the branch of mathematics known as real analysis.