What is the physical significance of y[n]=T{x[n]}

Q: -Find the value of th integral e-x' dx.

A: Consider I = ∫0∞e-x2 dx                              (1) Let x2 = t On differentiating both sides,…

Q: ! 6-Find the value of the integral * U x3/2 e-x dx

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Q: 1 x+1 Integrate: r21?

A: Here we have, I=∫01x+1x2+2x2dx

Q: Reducible to Homogenous method dy X-y-3 x-y-1 dx

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Q: 3. (a) Compute ,12x – 1| dx in two ways. i. By using properties of the definite integral and the…

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Q: 10. f (x) = x² + 4x + 4 Opens up/down:. Vertex: Axis of symmetry: Solution(s): y-int: Domain: Range:

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Q: Find the antiderivative of: xn+1 [(n + 1) In x – 1] if n+ -1 x" In x dx = (n + 1)² 1 (In x)² + C 2…

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Q: Find the linear approximation of f(x) = ln x at 1 and use it to estimate ln(1.33). L(x) In(1.33) =

A: Given : fx = lnx

Q: integral from 1 to 2 of (e1/x^3 ) / x4

A: To evaluate

Q: 3. Find a result by using homogenous for (x³ - 3x²y)dx- (x³y³)dy = 0

A: According to guidelines I have to provide answer only for  first qiestion...Thanks

Q: nd ifzxy+In(x) . x-r-I and y=e dt

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Q: 1 7. Evaluate the integral -dx using Simpson's method and also find the error comparing ó x +9 with…

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Q: 7. Evaluate the improper integral. -kx e (k: constant)

A: Please refer to the image below.

Q: 6 1) Find the general antiderivative for f(x) = 1+ x?

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Q: 1. Evaluate the integral |(x² - 5)e*dx 8.

A: Given that: ∫0∞ x2 -5e-3x dx To find: The value of the given integral. Let I = ∫0∞ (x2 -5)e-3x dx…

Q: 90% of it Suppose dy/dx = x-y and y = 2 when x 1, Use Euler's Method with increments of Ar = -0.1…

A: Given the differential      dydx=x-y with y(1)=2. Find y(0) using Euler's method with step size…

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: 5. Find the integral 1 -dx x -5x +6

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Q: 2. * S arctan x dx 1 In(x²) + C C 1. x arctan x C A x arctan x -In(x² + 1) + C -- B 1 D x arctan x…

A: Solve the given integration

Q: π/2 g(x) = 2x + 4 sin² x g(t) dt. - n 0

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Q: Q2: - If y = 3sec3t and x = etan3t prove that: - dy (In3)² dx y logy x * * -

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Q: Find the total differential z = 1/2 (ex2+y2− e−x2−y2)

A: The given function is z=12ex2+y2-e-x2-y2. Note that  ∂z∂x=12ex2+y22x-e-x2-y2-2x=xex2+y2-e-x2-y2…

Q: Find the linear approximation of f(x) = ln x at x = 1 and use it to estimate ln(1.34). L(x) =…

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Q: (b) Find the differential for y = -5 %3D

A: Giveny=4x-53   ...(1)

Q: 1. Discuss in detail the connections between differential and integral calculus.

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Q: Y 30 ΨΥ Ỉ2 2 47 13 23 24 με χ ΕΙΝΑΙ Fino η Exy. ἐκ ἔγ In ex² - (Ex)^ in [y- (fy) th nexy- έχτι…

A: Given information: X Y X^2 Y^2 XY 27 30 729 900 810 44 19 1936 361 836 32 24 1024 576 768…

Q: 2 3. Evaluate the integral ||x dx -2 O 2 4

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Q: 3. The integration of x e* with respect to x is: A. e2x. В. 2хе* С. 2

A: To integrate  xex2 with respect to x: ∫ xex2dx Apply u-substitution: u=x2 Differentiate both sides:…

Q: - Using Greens date $(x2 + y)dx bounding of the 0<x<1 and x' sysx.

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

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Q: 24. What does it mean to say that dV is an exact differential?

A: What do you mean by dV is an exact differential.

Q: 2. Evaluate the integral: 2xe-**dx -0

A: topic - integration

Q: 6. Evaluate the integral e* dx ex + e-x

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Q: Eliminate the arbitrary constants x = -ln t , y = at + bt^2

A: given  x=-ln t , y=at+bt2 claim- to eliminate the arbitrary constants

Q: 18. Show that Vxª + x and Vx* x→o by showing that they both grow at the same rate as x² as x' grow…

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Q: tion of the separable equation dy 23 3 +2)³ + 2)?

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Q: Jesaki Inc will sellN units of product after spending $a thousand in advertising, as given by N = 73…

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Q: The equation (y-x)=x(dy/dx) is Bernouli (y^n> 1) O linear in x O Homogenous O variable separable

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Q: se N.P.M. to estimate the root of -X = e -X for an initial of Xo =0

A: Here f(x)=e-x-x,  x0=0. We estimate the root of f(x)=0 by using N.R.M.

Q: I'm having trouble figuring out why the integral of e-3x dx is equal to (-1/3)e-3x. I do not know…

A: Given:    f(x) = e-3x

Q: Let y'=sinxy and y(0)=2 Approximate y(4) using Euler's method with step sizes of .25

A: The solution of a differential equation is defined as the function that satisfies the differential…

Q: 3 Evaluate the definite integral dx. (x- 5)4 -2

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Q: 13. Evaluate the integral dx x – 1

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Q: 39. Use Leibniz's Rule to find the value of x that maximizes the value of the integral px+3 1(5 – t)…

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Q: integral of C(1-e^(-bt)) with the initial time being 0

A: Let's find.

Q: y"+y = e" what is the nonhomogenous(particular) solution of the given differantial equation?

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Q: 4. Express the integral e-t tổ dt in terms of gamma function.

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Q: 1. Use algebraic manipulation and (if necessary) u-substitu- tion to integrate the function. (a) /…

A: Hey, since there are multiple questions posted, we will answer the first three subparts of the…

Q: ne differential ay of 'uonpuni y = V 5 - x2

A: