(5 Let f: [9,b]R be a Cont. function. Show that if fr-x)=-fro, xc[9,b), then & has at least one neal noot. 54

Q: Is it true that for cont. f So Si Axy)dydx = fS, Axy)dxdy| Justify your answer

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Q: Q:05 that the dual Space Show Co is of

A: The dual of c0  is l1  Let f=( f(1),f(2),f(3),...) ∈c0 and g=(g(1),g(2),g(3),...)∈l1.then  we claim…

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A: Given,        a(v, u)=∫-11(vxκux+vλu)dx

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A: Three functions f(x) , g(x) , h(x)are linearly independent if af(x)+bg(x)+ch(x) = 0 implies a=b=c=0…

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A: Topic = Functions   The intermediate value theorem states that if f is a continuous function whose…

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Q: Use the First Fundamental Theorem of Calculus to answer the ff. If F(x) = tvt +1 dt, evaluate F(1),…

A: Given: Now,          F(1)=∫11tt+1dt=0. Here,               F'(x)=xx+1⇒F'(1)=2 Further,…

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A: Differentiation is the rate of change in the value of dependent variable with respect to the change…

Q: Verify that fxy = fyx for the following funtion.  f(x,y) = ex + y + 1 fxy = ? fyx = ?

A: Given,            fx,y=ex+y+1

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A: Given : f'''t = t - 2cost

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A: As the function is square-integrable we will construct a Hilbert space having inner-product…

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Q: (a) Prove the following relation: B(x + 1, y): B(x,y) x + y %3D

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Q: Consider the function f (z) = e2: (a) Use the Cauchy-Riemann equations to show that f (z) is not…

A: The solution is given as

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A: Cauchy-Riemann conditions:  The complex valued function  f(z)=u(x,y)+iv(x,y) is analytic if it…

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A: Given that, f(x)=x2lnx and h=0.2. The three point formula for second derivative is given by,…

Q: 3. Show that f(z) = Re(z) is not analytic using the following two methods: Use the Cauchy-Riemann…

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Q: At which of the following points, the function f(z) = –3²15 –3z²15 is conformal? Check all the…

A: A function is called conformal at points where values of its first derivative is not equal to 0.

Q: Let F =. Find the lin , 0 <t< 2n.

A: Introduction: If f (t) is a smooth parameterization of an orientated curve for a≤t≤b If C is a…

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A: Using Cauchy Riemann Equation.

Q: If foxJ= S** t'dt, use the fundemental theorem of culcolus, part 1, to find f'cx) fixs=

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Q: Find f and f, and evaluate each at the given point y' f(x, у) arctan (2, -2) fx(x, y) = %3D fy(x, y)…

A: The  given function is f(x,y)=arctanyx,      arctanyx=tan-1yx and the point is 2, -2. Now we have to…

Q: F(X)=JX F: [o,2]-> show i fis lipschit z funcla or not find k to

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Q: show that the function fer fcx)= A - JX Satifl-y 2 the hypo theses of Roll's throrem on

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Q: Inlegrate the function f(x,9) -x,3zy over the rectungle R: e6x41 and sy61

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Q: Prove whether u(x, y) = x² – 2xy + y² is a harmonic function on a set D= {(x,y) | x < y}. I

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A: Hi! You have posted two non-related subparts. As nothing is specified, we are answering only the…

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Q: a). Determine whether Rolle's Theorem applies to f(x) = , on [-2,2]. %3D b). If so, find the…

A: Topic:- calculus

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Q: The range of the finction f(x, y) = In(-x² -+1) is %3D None of these O (00:0] O [0; +0) O [0;1]

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A: Here we will find out the required condition.

Q: The function f : R → R defined by f(x) = cos(x – 5) is а. one-to-one but not onto. b. onto but not…

A: Let's find.

Q: Which f (z) is not analytic at 0 ? 1 f(2) = z + 7 z2 o f(z) = z(z – 4) 1 f(2) = 1 o S(2) = , z-3

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Q: Find the value of c such that

A: Given∑n=0∞enc=7

Q: 3. Show that f(2) = Re(z) is not analytic using the following two methods: Use the Cauchy-Riemann…

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Q: If f is analytic and has a pole at z = a, then f(2)|| → 0 as z → a in any manner.

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Q: If f(z) u * 1V is an analytic function of z then prove that 2B. Əx?

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Q: 5.11. Prove that the function f(z) = Arg(z) is discontinuous at each %3D point on the nonpositive…

A: Solution

Q: inf f. is not measurable Vn. i

A: False ; is sequence of measurable functions fn is measurable then inf fn is measurable .

Q: Answer all the following questions 1. Find the doma in of f(x) = x-4

A: