It is not possible of an integral of a function to be zero over a contour although the function is not analytic inside the contour.

Q: 64. ● u(x) = (x² + 1)4*²-1 1 66. ●g(x) ex + e¬x

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Q: f(t) = {, - 2 2 -2

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Q: Find all the analytic functions for ReZ=Im f(z)

A: Find all the analytic functions for ReZ=Im f(z)

Q: Find two positive numbers whose product is a such that their sum is minimum.

A: Let the two numbers are x and y So, xy=a y=a/x   Their sum= S= x+y We have to minimize S

Q: S(1) = >1

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Q: d dx y' z' y" z"

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Q: lim , E C [2,4| 1/2

A: The solution are next step

Q: – dx x Inx x²+1

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Q: Find an analytic function whose real part is e-x (xsiny+ycosy)

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Q: Show that xy² cannot be real part of an analytic function.

A: Real part and Imaginary part of  analytic function is satisfying the harmonic.

Q: ((x+1)ª-y² Consider the function g(x, y) = {(x+1)4+y²' -1, if (x, y) # (-1,0) if (x, y) = (-1,0)…

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Q: if 01

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Q: Show that the function f defined by 1. (x, y) = (1, –1) f (x, y) : x² + y .2 (x, y) + (1, –1) x + Y…

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Q: Evaluate functio J dx x² - 6x + 13

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Q: colt)

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Q: 9. Calculate the triple integral of the function f (x, y, z) = e-(æ²+y²)(1–æ²–y²) over the region B…

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