d K, d1 + d. +... + K, 2 n K, K, 1 n

Q: 1. find the linear approximation to /(x) at x = Xg. Use the linear approximation to estimate the…

A: Linear approximation

Q: Q5. Let k > 0. Prove that if tm <x < tm+1; then т EGB (x) = E qB# (x). iEZ i=m-k Here B denotes the…

A: A spline of degree n is a piecewise polynomial function if degree k-1 in a variable x. The spline is…

Q: Use the information given in the figure below to construct a mathematical model for the number of…

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Q: =: (1)6 In(t)dt, 1, = e.

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Q: Which of the following is homogenous of smallest degree? x-y (A x-y В Inx - In y Vx+y x4+y4 D X

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Q: cot(nz) = 0 iff 1 + k. z = + kn. - KT. None of them z = k. + kT.

A: Let fx be any function then solution of equation fx=0 imply zeroes of the function .The zeroes of…

Q: Compute the discriminant D(x, y) of the function. S(x, y) = x' + y* - 6x – 2y² + 1 (Express numbers…

A: Given function f(x,y)=x3+y4-6x-2y2+1

Q: 4. If f:1 → R is differentiable on I and g(y) = yn for ne N and ye R what is (gof)' by usin chain…

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Q: 4. a) Compute P (P (0)) and P({{0.(0}}, {0}}). Show all steps of your cal- culation. b) Calculate…

A: Power Set : Let A be a set, then the power set of A denoted by ℘(A) and is given by set of all the…

Q: Use energy method to show that the following PDE p(x)un - [k(x)uz q(a)u, 0 0, u(0, x) = u(0,r) = 0,…

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Q: The value of Jo(0) + Jn(x) + J_n(x) is O a. 1+ J,(x) [1+ (-1)"] O b. J„(x) [1+ (-1)") Ос. 1-2J, (х)…

A: From bessels function results

Q: Let H(x)=0∫x√4−t^2 dt, for −2≤x≤2. a) Evaluate H(0) b) Evaluate H'(2) c) Use geometry to evaluate…

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Q: In the isosceles triangle ABC, AB=AC=5 units and BC=6 units. Find the location of the point D on the…

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Q: Q2. (a) Show that {e-*,xe-*} is a fundamental set of solutions of y" + 2y' + y = 0 on (0, 0). (b)…

A: Introduction: Wronskian of a given set of functions is very useful to examine whether the functions…

Q: Using the initial and boundary conditions solve Uxx - Utt = 0. c2 U(x,0) = 0, U, (x,0) = f(x) . U…

A: Given wave equation is. Uxx-1c2Utt=0Uxx=1c2Utt                            .......(1) Given boundary…

Q: Sa 1-rh+1 Prove that E-0 ar! F,r # 1 1-r ((n + 1)a,r = 1

A: For r not equal to 1,   The above given summation is geometric progression of first term=a and…

Q: ди 0 0 con ax2 at u (0, t) u (π, t) - 0 u(x, 0) = x 0<x<n %3D

A: Solution

Q: 2. Show that n n var ΣΧ) ΣΣον(Χ, X ). \i=1 i=1 j=1 Compare this formula with var(X+Y) = var X+var Y…

A: The equation is Var∑i=1nXi=∑i=1n∑j=1ncovXi, Xj.

Q: ldéntities will prove useful in achie Exercise 12. Show that E, (T: – ¤) = 0 %3D | E (*: – µ)² = E…

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Q: a. Determine the temperature u(x,t) in a rod given the following conditions: Rod length = L au = 0,…

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Q: 2. Find the r educed echelon form of the fo A = 0 0 0 6 54 0 (714161 Show your working

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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: - Proof that for an ODE of order n of the form y(n) + Pn(t)y(n-1) +.. + p2(t)y + P1 (t)y = 0 it's…

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Q: Residue of f (z) =, at z=0 equals e-2 %3D 23 O a. 3. O b. -1 8 O c. 1 O d. -1

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Q: Using Variation of Parameters compute the Wronskian of the following equation. y" – 2y' +1 = (x+…

A: we have to find the wronskian using variation of parameters

Q: 1. Fill in the following table. Give an integer for the order and YES, NO or N/A for all other…

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Q: a) Exaluate: %3D :(?)6 puo (x puif (9 and (3 +x x <O %3D for which f (x)=9). Give exact working out…

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Q: ind a function ƒ(x, y, z) such that Vƒ = (4z, 3y², 4x). Use symbolic notation and fractions where…

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Q: (a)Assume that after  w months,butterflies’populace  in 1000 is calculated as:…

A: Consider the given butterflies population:

Q: Current Attempt in Progress Use the given information to find Ax, Ay, and dy. y = V100 -x² ; x…

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Q: Use Euler's method to obtain a four-decimal approximation of the indicated value. Carry out the…

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Q: Given DE Cauchy-Euler xy +2y= Inx, x>0 what is the particular solution?? I. II. IV. Select one: O a.…

A: a. Given equation is  x2y''+2y=lnx Let x=et. Then differentiating w.r.t x,  etdtdx=1dtdx=e-t Now,…

Q: 59. Prove the general formula 1 I x – a)(x – b) where a, b are constants such that a # b. dx In х —…

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Q: iid, Let X1, , X"N(u,0²). Which is more efficient i, = X + }X,or îz =* (a) lz for n>5 (c )µz for all…

A: An estimator is said to efficient estimator if the variance of that estimator is less than the other…

Q: at to a o and terms of power senes' and opa apen n nlervas f Converganca dt t t. 2.

A: Given The given integral is ft=∫t1+t4dt Taylor series for fx=1+x+x2+x3+···=∑n=0∞xn, where x&lt;1. If…

Q: =Xtanx dk, Prove that ="IH (n+1)I,+(n-1) -1 T 1 2 n

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Q: Use Euler's method to obtain a four-decimal approximation of the indicated value. Carry out the…

A: Given differential equation.y' = x+y2, y(0)=0,.we have to find y(0.2) .we use Euler's method…

Q: Differentiate g(N) = rN| 1- with respect to N. Assume that K and r are positive constants. g'(N) = O

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Q: Write a in the form of a = a„T+a„N at t = 0 without finding T and N first if r(1)=(2+3¢+ 3¢°)i+(4+…

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Q: 3)if f(2)=1/z, has zero of order mat z=0, then f(z) has a zero of order m at d) e a) ∞⁰ b) 0 c) 2in²

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Q: Find the Wronskian Wly,, y2 Y3], where y, =t+6, Y2= sin(7 t), y3 = cos(7 t). a. -343 t-2058 b. 6…

A: The Wronskian Wy1 y2 y3   is given by,…

Q: Q1. Consider the two different losses: (i) zero/one loss where Ai dij = 1 and (ii) generic loss…

A: Given Consider the two different losses: (i) zero/one loss where A₁ = 0 and Aj = 1 and (ii) generic…

Q: 9: Find the Zero Cnd its た Aunction fに)、1にかi+Z+を。 Oroler

A: We know that, a function f(z)= (z-z0)n has zero at z0 of order n if f(z0)=0 at z0.

Q: orm of the operator A(x) = So (s3 + s² )æ(t)dt, where A : C[0, 1] → LI[0, 1].

A: Given integral operator is: ∫01s3+s2xtdt ; A : C0,1→L10,1

Q: Find the absolute maximum and minimum values of 2. 2 f(x,y) = x +y- 2x + 1on the unit disc x+ ys 1.

A: Given function is: fx,y=x2+y2-2x+1 and disc is: x2+y2≤1

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.