form" of the Fundamental Theorem of Calculus: Let f : [xo, x1] → R be a continuous function. Then if F : [x0,x1] → R is the function defined by the integral F(æ) = | s(t)dt, it follows that d F'(x) = dx f(t)dt = f(x).

Q: В. B. Show that the function f (z) = -i z2 is analytic.

A: The solution is given as

Q: 2. Use the First Fundamental Theorem of Calculus to differentiate the function f(r) = VI+ tª dt.

A: We will use the first fundamental theorem of calculus to evaluate the derivative.   The detailed…

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Q: Q3-A) Is the function F(Z) continuous or not at z-U? 1+|21,

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A: We have to find the analytic function

Q: Use Green's Theorem to evaluate F = (xy + y²)i+ (x – y)j | (1, 1) x = y² y = x² (0, 0)

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Q: Let esinx SoN f(t) dt and f is a continuous function, determine the value of f ()

A: If we have F(x)=∫0xf(t)dx then we have F'(x)=f(x). This is called the fundamental theorem of…

Q: Let f(2)=u+iv be an analytic function. Given that u=v² show that f(z) is a constant.

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Q: 3. Let X be a set. Call a subset A C X to be finitely complemental if its complement is either…

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Q: Construct an analytic function of the form f (z) = u + iv, where v is tan- (y/x), x # 0, y # 0

A: f(z)=u+iv where v=tan-1(yx)  We need to find the analytic function f(z)=u+iv  we apply Milne Thomson…

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A: The function of two variables  x and y will be of the form,   The function value of this kind of…

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A: Given vector funtion and

Q: Consider a function f given by А f(x, y) u(x) + iv(y). Determine all possible functions f of the…

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Q: (3) Let f be a positive and continuous function on [О, 1]. Сompute

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