1. Prove that C(n, r) = n!/r!(n – r)!

Q: The largest interval for which the IVP : (In(e - e?)) y + y = 1, y(5) = 0 has a unique solution is O…

A: We have to find largest interval for unique solution

Q: Suppose we have some approximation N(h) to M, and we know that N(h) = M + C¡h+ C2h² + C3h³ +0 (h*) .…

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Q: Evaluate the integral (2 + 6) (2? + 6z + 2)*dz by making the substitution u = x² + 6x + 2. + C

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Q: Using the Green's 2nd identity, prove that for 2-D Neumann exterior problems, O(In r) 09 Inr-0 dl .…

A: Consider the Green's second identity, ∭Du∆v-v∆udv=∬∂D=u∂v∂n-v∂u∂nds From the equation consider the…

Q: pany 2 = 355 3.24 = 0.52 on about these two co

A: The null and alternative hypothesis is as follows: Given: As the population standard deviation is…

Q: 1. Using the first prine =) , show that (1 – x*) + 4nxy = 0. %3D 2. If y = 1+x2, + qx2+rx +s passes…

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: Use the RK4 method with h = 0.1 to obtain a four-decimal approximation of the indicated value. У'%3…

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Q: Use substitutions to waite (In t)at, for seyo (1n ms of と in 0,9 € N, aE IR E IN, a E IR, a#0 where

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Q: (r+6)dr 4. S (z+2)?

A: Given: = The indefinite integral is, ∫(x+6)(x+2)2dx To find: -The complete solution of the given…

Q: While evaluating the approximate value of 1' dr, using Trapezoidal rule, taking h = 0.5, the N is =.…

A: Use formula for N

Q: die ktvaate et:rlrs erziv. 2l y=a* + &r-- 5+e" Kl) =

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Q: Evaluate the Integral dz 1. S z²+4z ANSWER: 1. - In + C 4 |z+4

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Q: eln (R/c) secx - sec?x)" sec(34 – x) "du?? dx to be integrable using the formula What should be the…

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Q: find Neumann senies for The solution of the integraL equation.- O go) - f6) +dSé g(4) dt %3D

A: Solution 1: Given integral equation is g(s)=f(s)+λ∫0ses-tg(t)dt Here k(s,t)=es-t Let k1(s,t)=k(s,t)…

Q: Use the RK4 method with h = 0.1 to obtain a four-decimal approximation to the indicated value. У'3…

A: The formula for finding y1 = y0 + 1/6(k1 + 2k2 + 2k3 +k4), and x1 = x0+h

Q: Show that F(n fla)] ds pleae do it frast

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Q: Prove that in the pairs of positive numbers ¤, y for æ² + y° = r the sum a+y is greatest when z = y.…

A: Here we solve the given problem of calculus.

Q: 3. (x³+xy²-y)dx + (y³+x²y+x)dy =0

A: We need to find the solution for (x3+xy2-y)dx+(y3+x2y+x)dy=0

Q: 2) Prove that: d? L„0) = n;(n – 1) %3D dx²

A: Consider the given information: Let Laguerre polynomial is given by, Lnx=∑k=0n(-1)kk!nkxk…

Q: The 300-lb block shown in the figure is kept from sliding down the inclined plane by friction and a…

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Q: What is the antiderivative of 1 / (x - (1/k)x^2) with respect to x? k is a constant

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Q: The largest interval for which the IVP : (In(e* – e²)) y' + y = 1, y(5) = 0 х —6 has a unique…

A: We need to find the largest interval for which the given IVP has the unique solution.

Q: (b) Show that I(n + 1) = n · I'(n), using integration by parts.

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Q: In the integration What is the value of u? xV1-4in?x a. u= 4ln² x In x b. u = 2 c. u = In x? d. u =…

A: The integration of the integral is  1/[x sqrt(1-4ln2x) ].

Q: B. Verify if the relatin O y= xe is a səlution to yl-2y'ty =o. y = eco( 2x) is a solution to…

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Q: +3 fn d the deivotive of this funckio slape of the tonpent On d the line ot (4,1).

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Q: Use the substitution formula to evaluate the integral. fin-√3/22 c2x dx 1 + e4x 28) 0

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Q: The DE : y' =e3x-7Y is seperable Select one: O True False

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Q: [5] Use the Gaussian quadrature to approximate the integral 1 x²e¬*dx. (a) Choose n = (b) Choose n =…

A: As per instruction we are allowed to answer only two sub questions. The generalised Gaussian…

Q: The value of c of fo-2- in the iterval .D such that rio--E) OA 3 OB. -3 OC 3 O0. 3-

A: c = 3explanation is given in below step

Q: The auxiliary (charasteristic) equation of the DE x²y" + xy' + y = 0 is %3D

A: Euler-Cauchy type differential equation: Let a equation x2y''+y=0 ..(i) Put y=xm in the given…

Q: In Exercise 5.8, we derived the fact that 4y1 Y2. 0< yı < 1,0 < y2 < 1, f(y1. y2) = 0. elsewhere.…

A: Compute the marginal density function of y1 using the formula: fy1=∫y2fy1,y2dy2 fy1=∫014y1y2dy2…

Q: 1. Is the following always true? If yes, clearly explain why. If no, give a specific counterexample…

A: Note: AS per our guideline we are supposed to answer only one question. Kindly repost the other…

Q: Find the indico 6. 2. 3+ 2 1..2+4+8+ 27 t. 4. 3. 12, (4)"- n= %3D1 2.

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Q: * السؤال The largest interval for which the IVP: (In(e* – e²)) y' + y = 1, y(5) = 0 has a unique…

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Q: Suponga P(Z,=K) = 2 Determine la distribucioñ de Zn. Ejercicio (DistrbugER del proceso de…

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Q: Evaluate the integral. 2 2 t+ dt 15 OA. 29 О В. 6

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Q: Evaluate plti 5. S z² dz using the formula [2² dz = A 3

A: This question is related to definite integration, we will solve it using given information.

Q: With integration by parts, J udv · Judv = UV - O True O False

A: Solve the following problem

Q: Use Euler-Maclaurin's formula to prove that E n %3D

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Q: (b) Let z = x + iy = re?". Find |z| and z² first in terms of x and y and then in terms of r and 0.…

A: Given:

Q: Evaluate by Cauchy’s integral formula: ∫ c e3z/(z+2)4dz where c: mode z = 4.

A: To find - Evaluate by Cauchy's Integral formula : ∫Ce3zz + 24 dz where C : z = 4     Formula used -…

Q: E valvate cox³ (x²+3)dx 2.

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Q: Then show that N(A) = R(AT)+ and N(AT) = R(A)+. %3D 11-1 02-3 -1 1-2 N(A) = N(AT) =

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Q: Which condition would prove AJKL - AXYZ? K Y 56 7. JL XZ 造=8 KL 8 JK %3D XY

A: We have to find which condition would prove ∆JKL~∆XYZ.