If H(r) = 1- 3.r – 3.r2 +6.x is the Hermite interpolation for %3D 0 1 the data in the table f(r) b1 then f'(x) -3 c

Q: Given X= 4Y + 5 and Y = KX + 4 are the lines of %3D regression of X on Y and Y on X respectively. If…

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Q: (у — х + хусot x)dx + xdy 3D 0

A: Given: Linear First Order: y-x+xy cotx dx+x dy=0 We have to find a general solution to the ODE.

Q: Question 3 a) Develop a first order method tor for approXivaating t' (x) which uses the data f…

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Q: Q2) The critical points of the function F(x,y) = x + 3xy + y3 O (0,5) O (1,0) none of others O (1,1)…

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Q: If L(x)=mx+b is the linearization of f(x)=2x³ - x +3 at x-1, then m= Using L to approximate 2(1.01)…

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Q: Find the general solution by using reduction of order method to ty" – (t + 1)y' + y = 0 given that…

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Q: given eady ds ignes ive is 1. 1 y" + 3y' + 2y = 6 + e* The next Wronskians to calculate use y, = e*…

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Q: az Suppose z is a function of r and y, and csc Vr² + yz = 2"e»in z_ Solve for dz and dy

A: Given: csc x2+yz=zyesin x To find ∂z∂x and ∂z∂y.

Q: For the following linear nonhomogeneous ODE y' + p(x)y = r(x) cos x If S p(x) dx = In|x| and r(x):…

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Q: The residual of ŷ; is defined by e, = y, – ĝ.. (1) Prove Σ -0 and Σiι u ΣΗ. (2) Prove E1 T;ei = 0…

A: (1) In problem 1 we have to prove that : a) The sum of residuals in regression model that contain an…

Q: In each of the following problems, find the Wronskian W(y1,y2)(x) of the given list of functions and…

A: By using determinant and derivative of functions we solve the given problem.

Q: (b) Determine e so that п п c£[(x; - X;)² i=l j=1 is an unbiased estimator of o². s2 ogunl to

A: 6. From the given information, X1,.....,Xn~f be an iid random sample with mean μ and variance σ2. a)…

Q: Let X1, ·.. , X, " f (x;0) = e-=/°, x > 0. (i) Find the sCore and information functions of 0. (i)…

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Q: For the following linear nonhomogeneous ODE y' + p(x)y = r(x) cos x If S p(x) dx = In|x| and r(x)…

A: Given y'=pxy=rxwith ∫pxdx= lnx; rx=cos xxIntegrating factor , IF =e∫pxdx=elnx=xThe solution to…

Q: ate the order of the given (1-x)y" - 3xy' + 6y = cos x etermine whether the equation is linear or…

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Q: If u(x) = 19 is the standard integrating factor to (x-8) y' +5 g(x) y = x²-4, find g(x). x+27…

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Q: Find solution of an equation X f(x) 1.0000 1 1.25 0.8000 1.50 0.6667 1.75 0.5714 2.0 0.5000 a. Using…

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Q: Calculate coeff. of Q.D. and Bowley's coeff. of skewness from the data given below : Profits No. of…

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Q: If g(x)=- A B d- ſ ^ [e' − In(2t + 1) ]dt, find g*'(x) . dx -2 2 (2x + 1)² 4 et + (2x + 1)²…

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Q: The homogenous D. E. with constant coefficient of at least order which has the solution y = 2x? +…

A: Using diffenrentiation

Q: Let X ~ T(a, B). If E(X) = aß and E(X²) = aß² + a² ß². If â = X, find the method of B moments…

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Q: Let µ(x)= e8x" be the standard integrating factor to x y' +p(x) y = x³. Find p(6).

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Q: Q1-Find dy / dx for the following functions : e0 -2 2.8ln2 Y: Cosh9x * Inxy 4 6. cos0 log2 2 Q2-…

A: By bartleby rules, only Q1 has been answered.  Given function is…

Q: Suppose there is no known formula for g(x), but we know that g(2) = -1 and d (z) = V2 +5 for all x.…

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Q: The coefficient of correlation between X and Y is - and o = a, of = 4a, and %3D %3D ož = 114 where Z…

A: Given: Z=3X-4Y. The coefficient of correlation between X and Y is 13and σx2=a, σy2=4a,σz2=114

Q: If p(х, у) %3 х" у"is an integratingfactor of the the DE. (12 + 5ху)dx + (6х у-1 + 3х2 jdy %3 0…

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Q: 5. Test the ff ODE for exactness and find the general solution of the DE (2x + 3y) dx + (3x + 4y)…

A: To solve Differential equation.

Q: If f(x) =x - r- 3x+6, what are the critical value(s) of f(x)? (a) x only (b) x=3 only (c) x=-,,x=ì,…

A: Consider the given fx=23x3-52x2-3x+6

Q: 4. In one model of the changing population P(t) of a community, it is assumed -, where and are the…

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Q: 3. In the linear regression model Y₁ Bo+B₁X₁+Ei, an alternate estimator Y Â₁=X. State all the CLRM…

A: x explanatory variable y Dependent variable The equation of the linear model is y = β0+β1xi+εi…

Q: 2. Find a particular solution to each of these ODES by using the method of variation of parameters:…

A: Note: as per our guidelines we have to solve 1st question. So please repost other questiin . sorry…

Q: If y1 (x) = cos(x) is a solution of the D. E.: xy" - 2p(x)y + q(x)y = 0, where x > 0, and p(x) and…

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Q: The standard form of 3dy-xydx= 3y³e/3 by Bernoulli's ec 4x/3 dx 3 A dy ху = 3e**/3y3 dx 3 'x=…

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Q: 2. Consider the model: Y, =0.2Y+e,+0.4e. Find the autocorrelation function p, for k=1,2,3.

A: We are required to find autocorrelation function(acf) of an ARMA model.

Q: Consider the following ODE system: = x² + xy³ =zy subject to the initial conditions x(0) = 2 and…

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Q: Given that X has pmf f(x)=1/(2)^(x+1) , x=0,1,2,... and et<2 , use mgf technique to…

A: Given: X has the pmf as follows, f(x)=1/(2)^(x+1) , x=0,1,2,...et&lt;2

Q: 1 be the standard integrating factor to y' + p(x) y = q(x). If y, =7 x2+19 x+ 19 is one of its…

A: Given: The equation is: y'+pxy=qx The standard integrating factor is: μx=1x And, solution is…

Q: d If g (x) = ª[e' - In(21 + 1)]dt, find g(x) . dx A e-In(2x+1) 4 (В et + (2x + 1)² 2 (C) (2x + 1)² 4…

A: Topic:- application of integration

Q: If y, (x) = e** is a solution of the D.E y" + p(x)y' + q(x)y = 0, where p(x) and q(x) are continuous…

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Q: 3. Let g(x) = V10- cos(x) +3x. %3D 3.1. Find g'(x). 3.2. Find the linear approximation to g(x) at x…

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Q: What is the largest step-size that can be used for a stable solution to the follo higher-order ODE…

A: Given:

Q: The general solution of 2y" -xy'+ (x - 24 ly = 0, is: OaC,xJ,) + C,xJ_(2) OcC,,(3) + C,xJ_(3x)…

A: The given equation is  x2y"-xy'+x2-24y=0                                  (1) The differential…

Q: Consider the Bernoulli I.V.P ry'- x²y" = y, y(1) =1. where n-5. Let v= y" be the substitution that…

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Q: Suppose that we don't have a formula for g(x) but we know that g(1) = -4 and g'(x) = V x2 + 15 for…

A: g(1)=-4, g'(x)=x2+15 Finding the value of g '(1) g '(1)=12+15=1+15=16=4

Q: For the AR(2) process Y, = (1/3)Y–1+(2/9)Y-2+ Et, find the autocorrelation function of Y; and…

A: Given the AR(2) process as Yt=13Yt-1+29Yt-2+εt

Q: If we use a linear approximation of e- at a = 0 to approximate e-1/3, then we obtain: А. 4/3. В. 2/3…

A: The solution is given below

Q: Find the general solution of the given ODE. * (x+y-1)dx - (x + y)dy = 0 x+y+ ln |2x + 2y - 1|= C…

A: The given ODE:x+y-1dx-x+ydy=0.We need to solve the above ODE.

Q: 9. Find for each of the given functions using the chain rule. dx a. y = (4x + 3)3 b. y = v6 + x2 -…

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Q: If (х, у) %3D х" у"is an integratingfactor of the the DE. (1+ 3ху)dx + (ху-1 +x?)dy %3 0 Then, the…

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Q: se Euler method to compute ys for the DE yy'=2 x for y(1)=3

A: Euler's Method

Power Operation

Power operation is topic of algebra in Math. It is use to represent repeated multiplication. Very big number and very small number can be easily express using power operation. Power operation is useful in many fields. In space engineering, it helps in representing the distance or size of particular heavenly body. In medical field, it is used to represent very small size. In medical field it helps to mention size of bacteria or virus. 

Exponents

The exponent or power or index of a variable/number is the number of times that variable/number is multiplied by itself.