{; .0 < x < 2 f(x) 2 , x > 2 FİND THE LAPLACE TRANSFORM OF THE FUNCTİON WİTH THE HELP OF THE DEFİNİTİON .(DEFİNİTİON MADE BY THE İMPROPER İNTEGRAL)

Q: MTH 32 (3) What is the Definite Integral of a function f from a to b?

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Q: Evaluate the given Laplace transforms. (Write your answer as a function of s.) L{1} %3D L{t} Use…

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Q: /find the Fourier integral representation of the given function. x0 -x le

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Q: Evaluate the definite integral by the limit definition

A: Here,

Q: (e-2º sin5t) dt4

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Q: 1. Verify Rolle's theorem for the function (x+2)' (x-3)* in the interval [-2,3]. Plot the curve…

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Q: L[2t2 + 5 – 3 cos nt), t > 0

A: We use the Linearity property and table of Laplace transform to find the answer of the given…

Q: Which of the following are needed to transform the parent reciprocal function f (x) = 1/x so that…

A: Graphical transformation

Q: Differentiate the following function In z I y = 0 - 1/1/(x-²) I 1-ln z O O 1-r ln r r³ 0 1 I

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Q: (b)Evaluate the integral directly we-wdw

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Q: Use the convolution theorem to find the inverse Laplace transform of the given function. Laplace…

A: We will find out the required value.

Q: Uncover the function f shown that the slope of the tangent line to the chart of f at any point (x,…

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Q: Use differentials and the graph of f to approximate (a) f (1.9) and (b) f (2.04). To print an…

A: To calculate the approximate value of a) f(1.9) and b) f(2.04)

Q: Sketch the domain of the function f(x, y) = lnty-1 + /1-x² - y² + sin(xy).

A: Domain: The domain of the real valued function is the set of all the values for which the function…

Q: What is the indefinite integral of this function?  f (z) = √z (4(z-1)2 + 1/z3)

A: What is the indefinite integral of this function?  f (z) = √z (4(z-1)2 + 1/z3)

Q: Prove that x''' + yul + zm2 = where dashes denote differentiation w.r.t.s. 1 22 + 1 + p" p* -176 402

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Q: rt01+sin x +00 -dx x2

A: Here we will use  integration by parts  ∫uv dx= u ∫v dx -∫dudx∫vdxdx

Q: sin*(¿e) cos* (e)də

A: This is a problem of indefinite integral. Based on the general formula of trigonometry we will…

Q: 1. Given the function f(x)=x -8 on [0,6] a. Sketch the function. b. Use the definition of the…

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Q: f(x)= 0, x 1

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Q: Find the convolution (f * g), after integrating find the Laplace transform of (f * g): f(t) = cos2t,…

A: We have to find convolution (f*g) and the Laplace transform of (f*g) wheref(t)= cos2t, g(t)= et .

Q: Where is Log(z2 + 2) holomorphic (Analytic ) function ?

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Limits of Multivariable Functions

Multivariable calculus is an extension of single variable calculus. It involves several variables instead of just one. Assume there is an open set containing points (x0, y0), let f be a function defined in that open interval except for the points (x0, y0). The multivariable limit of this function as it approaches the points (x0, y0) and is denoted as: