Given x (0) -2,x (1) =1, x (2) =2 evaluate X(k) by using DFT.

Q: Find the general antiderivative of 4 2 + x3 f(x) = x³ + 6/ | + C

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Q: Find e* + x-2 + C e* – 1+ C + C (1/2)x² e* – In |x| + C

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Q: (x2 – 1)y" – 2xy' + 2y = 0 - tion ofS the o uation

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Q: 7. Differentiate a) f(x) = ev==t and b) h(x)= (5x² – 8r)e**-4". %3D

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Q: Show that kT| e-t²/kTdt = (kT)3/2 " 0. 2

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Q: sion By A knawn x²-5x_x+5 ーちメメ -X cr ar

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Q: Calculate ∂ω/∂x for ω=e^−2x x(multiplied by) e^(z^2y)

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Q: Find the linearization of y = eV3x at x = 64. (Use symbolic notation and fractions where needed.)…

A: Solution: The objective is to find linearization of the given function

Q: 4.2 Apply the appropriate method to calculate the following: 1 = f***-8 I = S x2-4

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Q: dæ Evaluate: x/9x² +4 A) None of the above V9x² + 4 + 2 B f (x) = -2 ln +C %3D 3x © s(12) = -- In f…

A: I=∫dxx9x2+49x2+4=t9x  dx9x2+4=dtdx=9x2+49x dtI=∫19x2 duI=∫1u2-4 duI=∫1(u-2)(u+2)…

Q: Consider x = 3x1 – 2x2, x, = 2x1 – 2x2, with x (0) = 3, x2 (0) = ;. b If x1 ge + e-, find the values…

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Q: Find a general formula for dr ax + b dx" cx +d

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Q: (e) Yk+1 +Yk = 1/k(k+1),

A: Given, yk+1+yk=1kk+1Substitute:yk+1=y'yk=yEquation formed is:y'+y=1kk+1A first order separable ODE…

Q: 1. Employ Bairstow's method t

A: f(x)=9.34-21.97x+16.3x2-3.704x3Initial guesses of r=1, s=-1 and…

Q: 2. A counterexample can be used in all of the following situations except?

A: A counterexample is a particular case that demonstrates the falseness of a general argument.

Q: kx 4+x² If k > 1, evaluate O ka -In|x² + 4 +C 2 Okx -arctan (2x) + C 2 Ok In(x² + 4) + C O arctan…

A: Given: I=∫kx4+x2dx   ...1   As we know the common integral. ∫1ax+bdx=1alnax+b+C

Q: The following table shows the result of inoculation against cholera: Not Attacked Attacked 5 (AB) 9…

A: Hypotheses: H1:The effect of inoculation and Cholera are independent Ha:The effect of inoculation…

Q: Find the general solution to the Bernoulli-type ODE x²y' + 2xy = y°, for x > 0.

A: Bernoulli's equation is a special type of first-order linear ordinary differential equation. When…

Q: 3. Derive the reductive formula for S sec" (x) dx.

A: We will find out the required solution.

Q: By using the substitution u = 4x + 1, evaluate (4x+1) dx 1 x²+x+k 4 4x2 + x + k 1 x' + x + k (4x +…

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Q: Find g'cx) gon= XX dx

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Q: SAS K Y %23

A: Given figure, we have to state the congruence required to prove the congruence of triangles using…

Q: Calculate ∂ω/∂z for ω=e-2xe (z^2y)

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Q: The function f(x) = X = (6x 3) e5 has one critical number. Find it.

A: Given function ,   f(x)=(6x-3)e5x

Q: Find G'(x) In(8) (4e 6t 1) dt G(x) х G'(x)

A: Given,

Q: at k ( k) = n(k-₁) fo 1) for in

A: To prove, knk=nn-1k-1

Q: O': Find the general yy' – 2y² = e²

A: A first order Bernoulli ordinary differential equation is of the form dydx+pxy=qxyn Where p(x) and…

Q: :Q3 Classify PDEs below и ди y2 и + и = ue 5x — - ду

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Q: да Given zTan¯¹ (x + y) — ln [1 + (x + y)²] = 5%, what is ду -1 2-2x-2y none of the choices 2- 2x +…

A: ∂∂xtan-1x=11+x2 Note : As per our Guidelines , we can solve first question. Please repost remaining…

Q: Find the general antiderivative of f(x) = = + C -28²³-03-2/3 + √²

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Q: Consider z=e (*3+y2) Evaluate dx2 O (6r2+ 3x)e (*3+y2) (9x4+6x)e (x³+y²) (6x4+ 9x) e (x³+y²)

A: Topic = Derivative

Q: 6) Find most general antiderivative of the fxn. a) f(6) = x5+2x²-1 X' B) 4(1) - 2 +30*

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Q: 1. If the pdf is 2x-2/K e^8x-4x^2 , 0 < x < 1 Find K.

A: 1. The pdf is given by  We know that,

Q: I Findk the GS op the bE (x+3y)kk +(3x+g-) dy mo 50

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Q: Find y''of 4cos(x/2)+e^-2x

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Q: 48xyz < (3x + 2y)(y+ z)(3x + 2z) for every x, y, z E [0, +∞[.

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Q: Show that So e-ax J₁ (bx) dx= 1 √(a³ + b³)³ (a > 0)

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Q: x2+x-2 dx If S (x²–1)(2x-x²) dx can be resolved into AS+ B ƒ f(x)dx + D S g(x)dx , then Lif(x)dx –…

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Q: Find (5x - x²)e* dx O(x2 -5x)e-x-(2x - 5)e¯X – 2e-*+c O (5x-x2)e*- (5 – 2x)e* +2e* O (x2-5x)e*- (2x…

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Q: If L, f(x)dx = 18; L, g(x)dx = 5; and ſ, h(x)dx = -11 , evaluate ,[ƒ(x) + g(x) – h(x) ]dx. %3D

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Q: f Lan 2X e *3 of +sec2X Pinel dy o

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Q: x = y + Z y² = 0.000396707 - 0.24576 x2 z* = 0.00029753 – 0.12288 x²

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Q: Given G(x) = jin(2t+1)dt , find G '(x). O In(2x + 1) O In(2x + 1) - In3 O In(2t + 1) + C 2 2x+1

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Q: Given that n2 1 and xn =V 4n² + 3n – 2n Will {Xn}, be divergent or convergent? n=1 Will E-1 Xn be…

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Q: Does y =e9-x2-2 exist?

A: Given an equation, y=e9-x2-2. To check whether the equation exists or not. The value of e is…

Q: Find the linearization of y = eV3x у at x = 64. (Use symbolic notation and fractions where needed.)…

A: topic- linearization of a function

Q: Find the general solution of the given ODE * 3x+2y

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Q: 5. y = xArctanx - In V1+x 6. y = In (e* + e*)

A: topic-second derivative of a function

Q: (b) Evaluate |(2x+3)V x² + 3x – 5 dx , by using substitution method.

A:

Statements and Logic

Logic is the analysis of general patterns of thoughts without regard to any specific sense of context.