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Q: 14. Consider that * Sof (x)dx = 2 and f'(1) = 3. Find Soxf"(x)dx. %3D 3 O 5 O 1 O 4 O 2

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Q: s given by L2)- by L)= this income m Suppoce the Lorenz cunve for a country is 1-- Determine the…

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Q: 7) if p(X) =- ) , and grea) =0; g'LW)=), Find f'la). %3D

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Q: Q Find the deriva tive using the de fini tion (x)

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Q: Suppose p is true, q is true, r is true, s is false. Then (-pvs) v (SAr) is T/F? A) True

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Q: 2 Exercise.8 Find: P4 (x), Pg(x), L P¾(x) P3(x) dx , LIP,(x)|² dx

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Q: If f(x) = exp(-x).In(x), then , when x=1, df/dx is 1/e C 2/e O e nonexistent O

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Q: The IVP is well-posed if f(t,y) =y satisfies the Lipschitz condition. Select one: O True O False

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Q: find the critical points:

A: Given function is  and the interval isThe critical points of a function are obtained when the first…

Q: и(х) -f(x) 1(x) 1.5 + 2 3 4 In the figure, is f(x) squeezed by u(x) and (x) O 1. at x = = 3? ? 2. at…

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Q: What is the range of the function x) = X-3 O{xÎR|x'0} OIvIRly! 0} O tyÎRIy1 3} O{xIR|x'0}

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Q: れお! /0 fi23)=4 4 (か) 2,十 F) Eanals it Ofiles)= 12 D Not if tha above

A: Given: Fx,y = x3y2 To find: Fx2,3 We know that Fxx,y is differentiation of Fx,y with respect to x ,…

Q: The Ideal Gas Law states that PV = nRT where P is pressure, V is volume, n is the number of moles of…

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Q: 3. If f(x, y, z)= In xyz te(3.0²), find f,,f, and f-· 4

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Q: Let f(2)=³ and let C = {z € C : |z| = 1}, described in the positive sense. Determine the value of Ac…

A: Given that             fz=z4-5z2      and    C=z∈ℂ : z=1.

Q: 2. Estimate the value of V22. + • V22 is between and but closer to Decimal estimate: 22-

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Q: 2 1 The approximation of -dx by the composite Trapezoidal Rule with n=2 is O x+4 0.30833 0.40833…

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Q: The approximation of x' e¯*dx by Simpson's Rule is O 0.162402 O 0.160603 O 0.160602 O None of these…

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Q: QUESTION The minimum value of n required to approximate xedx by composite Trapezoidal rule with an…

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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: Suppose that a) [15x²y; 0<x<y<1 f(x, y) = { 0; otherwise. Compute E(Xy), Var(X) and Var(Y). b)…

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Q: Find f '(x) if f (x) = / (In z) (e*=*). (2) = (Ina) (et)) (Ina) (e*") (80)(8) + (e*") (:)) (In z) (e…

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Q: 7. Given that f(z) = ar/² ++c*, find f'(x) .

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Q: ronskian of the DE : xp(x)y' + 3y = 0 = er² et? et?

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Q: 2. Let X~N(u, o2). Show that the MGF of X is etHtc²a².

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Q: In Exercises 5–12, find and sketch the domain for each function

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Q: (14) Approximate S, x² ex², Using Simpson's rule dp,

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Q: - Given y= ela's -x²-In'r, what is y'?

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Q: Man of X = Avenge f= ELK) H.w prove that E (x-x) =0 Hint 又=E(x)

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Q: B/let Flx)=[X]-X,x E(-2,2).which valuesof x o E(X) continuaus?

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Q: (a) Given that f(u) = u° +1 and u= g(x) = /x %3D Find the value of (ƒ o g)' at x = 1.

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Q: Q4. Evaluate ſ In(x + v1 +x²)dx

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Q: 31. Evaluate , f(x) dx given that f(x) dx = 3, 2 f(x) dx = -2, and f(x) dx = 5. %3D

A: Given ∫−11f(x)dx=3∫23f(x)dx=−2∫13f(x)dx=5 To find: ∫−12f(x)dx

Q: We hae a theorem that offers conditions when the IVP: x'- f(t, x), x(to) = X , has a unique…

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Q: 7 Gi ven that / f(z)dz =, what is / f(r)dr? 3'

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Q: 10- If f(u, v, w) is differentiable and u = x - y, v = y - z, and w = z - x, show that fe fe fe = 0.…

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Q: Find fCx) if flo)=0 and the tanGat (k,F CX) has ine af Slore x(x+2) a

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Q: 2. We want to evaluate e¹/x dx using the composite trapezoidal rule with three decimal precision,…

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Q: 2 1. Use Simpson's rule to evaluate | dx , by taking n=4 o V1 + x* 2.Find the Area, enclosed by the…

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Q: Use the TRAPEZOIDAL with 3 level Romberg (k = 3) to evaluate: e* sin x , 1+x²

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Q: 19 When approximating / f(x) dx with 10 rectangles, what is Ax? 1.8 18 O 19 10 1.9

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Q: Q2-Prove that = va* – x² ify= ()sin () + () va² - x* = va² – x* if y = (;")sin*+ (4) + () Va² - x²

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Rate of Change

The relation between two quantities which displays how much greater one quantity is than another is called ratio.

Slope

The change in the vertical distances is known as the rise and the change in the horizontal distances is known as the run. So, the rise divided by run is nothing but a slope value. It is calculated with simple algebraic equations as: