Let f be holomorphic in a domains containing the closed unit disk D(0, 1). Let S = S (0, 1). Show that 1 f(0) + f'(0) = 2ni f(w)e" dw. w2

Q: (3) Evaluate the integral F. dr where the vector F is defined by F = and where the curve C is…

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Q: Assume that u and u are continuously differentiable functions. Using Green's theorem, prove that Uz…

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Q: Consider the function F(x, y, z)=(√√1 - x² - y², ln(e² - z2²)). (a) This function is a mapping from…

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Q: Show that the function given by f(x,y)= x² + 3xy is differentiable at every poin using the…

A: Introduction: Distinctiveness (differentiability) implies continuity. If a function is…

Q: Find B and t for the space curve r(t) = N 11 ਕਰਜ |·+|· 1 +1 + 2 3 ()+( 3 +1 j, t> 0.

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Q: Q3(a). Let f(z) be analytic in the unit disk |z|<1, if f')(0)= f® (0)= f(5)(0)==0. Then, prove that…

A: Since f(z) is analytic in unit disk. So we can express f(z)  can be expressed as Taylor Series.…

Q: 1.T.2 Let V be the set of all twice-differentiable functions f : R → R satisfying f"(x) = f(x) – 5.…

A: Let, f and g be two functions in V.  Then,        f"(x) = f(x) - 5       g"(x) = g(x) - 5.

Q: 8. Given the space curve C as the image of the vector valued function r(t) = 2ti+t³j+-t-¹ k OR r(t)…

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Q: Find r'(t), r(t), and r'(t,) for the given value of to: Then sketch the space curve represented by…

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Q: Let z = ƒ(x, y), x = g(s, t), and y = h(s, t). Explain how to find ∂z/∂t.

A: Solution:- The given question is  Let z = ƒ(x, y), x = g(s, t), and y = h(s, t). Explain how to find…

Q: 2.) Are the following functions vector-valued or scalar-valued? a) f(u,v, w) = Cu²v, we, sv) b.j…

A: Answer given below.

Q: Match the space curves in the figure below with the following vector-valued functions: O A. r(t) =…

A: See that options ,  A )  r ( t ) = &lt; 1 , t , t &gt;  If we consider the first two coordinates ,…

Q: a) Show that if u, v, and w are differentiable vector functions of t, then d du V X w +u - dt dv dw…

A: According to our guideline we are supposed to answer only one asked question.kindly repost other…

Q: Let f : R2 → R is a differentiable function at point a. (a) Let w, v ∈ S1:= {(x, y) ∈ R2 | x2 + y2=…

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Q: Let f : R" → R be a continuously differentiable function, while æ € R" is its non-stationary point…

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Q: real vector-valued function such that r" exists. [r(t) x r' (t)] = r"(t) × −3r(t). dt Let r be a…

A: USING THE CROSS PRODUCT OF TWO MATRIX METHOD, FIND BOTH SIDES SEPARATELY,WE GET