8. If P(x) = Vx h show that P(x + h) – P(x) = %3D yx+h+ yx

Q: 4. Find the particular solution of y(x² + y²)dx + x(3x² – 5y²)dy ;where x = 2 and y = 1. -

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Q: 3. The Critical Point of y=xe*

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Q: Example 2: Find the particular solution of (x – y)dx + (3x+y)dy = 0 when x = 2 & y = -1.

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Q: 3. Find the particular solution of the differen- tial equation: (x² +y² )dy=xydx, given that x=1…

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Q: If T, is an MVUE of y (0) and T, is any other unbiased estimator of y (0) with efficiency e < 1,…

A: Answer: For the given data,

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A: Explained below

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Q: 1. (a) Show that (x) x² is an explicit solution to dy X- = 2y dx on the interval (-∞, ∞). (b) Show…

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Q: •1 cln(5) 1- S SmS) xy evx ´dydx r

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Q: 13 and 17

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Q: 2+ Problem 3/ Evaluate z*dz along the line y=

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Q: et Xi- Nco,1) and n=2 T=X,+Xz Show that Tis Sufficiencs y Statistic

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Q: S x2 +2x-10 (2x+4) + 1 JE + 4x +5) Consider dx = x² (x² + 4x + 5) (2x+4) + 1 dx- x² + 4x +5 dx ,…

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A: Explanation of the answer is as follows

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Q: 5. Find the General and Particular solution of 2 = 3y ; y = 3, when x = 0 dy dx

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Q: 16. (x – y ln y + y ln x) dx + x(ln y – In x) dy = 0. ) In

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Q: II z= ě Y x - Juv Find dz dv üs ing chein rule.

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Q: 1. S 2xe2*dx

A: Given that,   Using integration by part

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Q: Consider the initial value problem {y′−3y=6, {y(0)=1. What is the limit of y(x) as x approaches −∞?

A: