f(z) =z2 is discontinuous in C

Q: (a) Show that y for the given z = e" In x+ xy

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Q: If f(x.y) = In(x² + y²) + find fr and fy -

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Q: Find the linearization of x+1 f(x) = 2 – dt 1 + t“ at x = 1.

A: Given function is

Q: Find an upper bound for ||L|| where L: R² → R³ with L(x, y) = (2x + y,x + 3y, 3x – 2y) -

A: Here we use the definition of boundedness of a linear operator.

Q: 2. If f (x) = Sn* et? 0, dt, find f'(x) V2t+sect

A: The solution is given as

Q: If L(x)=mx+b is the linearization of f(x)=2x³ - x +3 at x-1, then m= Using L to approximate 2(1.01)…

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Q: -Find the D.f ofr (x, y) = (x² – y)' at Po(3, 1) with

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Q: Let f(x,y)=-x³+4xy-2y²+1; find the critical points of f and test them using D=D(x,y).

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Q: Verify Young's Theorem y? x2 z = In(2x + y) + +e(x+2y) y

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Q: 1. If f(x, y)=3x' cos y– y sin x– 2.x In y- yln x-4x²y, find ôf ôf d²ƒ _ô²ƒ

A: According to question given thatf(x,y)=3x3 cosy-y2 sinx-2x ln(y)-y ln(x)-4x2y

Q: Find the linearization of g(x) = 3 + sec (t - 1) dt at x = -1.

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Q: Find the linearization of f(x) = 9 – dt at x = 1. 2+t

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Q: If L(x)=mx+b is the linearization of f(x) 2x-x +3 at x-1, then m3 Using L to approximate 2(1.01)…

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Q: d Use the chain rule to calculate f(x), if f(x) dx, dt. -x12 f(x) =

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Q: 2. Find frxz for f(x, y,z)= z² e³xy

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Q: Find the linear approximation L (x) to ƒ (x) = xcosx at a = T.

A: Given that, f(x) = x cosx and we have to find linear approximation L(x) at a = π

Q: 7. Let f(x, y) = 10xy* + x°y². Find fyyy. 4

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Q: If f* f(t) dt O 6 1 O -4 divergent = 20x √4x²+21 ∞ -4, then f(t)dt is X

A: Given

Q: 교꾸가고 (a, y) + (0,0) (x, y) = (0,0) f(x, y) = x2+y2 is discontinuous at (0,0).

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Q: x+2 32 dt at x = 4. 2+t 6 Find the linearization of f(x) = 3-

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Q: Determine the linear approximation of f(x) = x' at x = 1. О а. уз- 1 х-0 О Б. у3 1x +0 O c. Not in…

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Q: Find the ditterential of the function y = (x + 1(5x - 3). Sx-x-5 dy = (Sx - 3) *?+ 6x-5 (5x- 3)? dy…

A: Use the quotient rule of differentiation ddxuv=vdudx-udvdxv2. Power rule of differentiation…

Q: 1. Show (in terms of e- 6) that a function f : R + R defined by f(1. y. 2) = (2x + 3y + 42) is…

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Q: 4. Use the linearization of f(x, y) Vx + 2y to approximate f(3.01,2

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Q: If A(x)= f(t)dt is increasing on [0,10], then f(x) must be increasing on [0,10].

A: Given,A(x)=∫0x f(t) dt

Q: d) The function +(xy)-r*r2y) exp G 18xy is homogencous in of degree X and

A: The given function is: f(x,y)=(x2+2y)e2xy+8xy...(1) The function f(x,y) is said to be homogeneous…

Q: Determine the linear approximation of f(x) = =ª at æ = 1. O a. y=- 4x-3 O b. Not in the list O c. y=…

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Q: Find f(t). s(s + 1).

A: L-1[F(s−a)]=eatf(t) From first shifting property, L{e^(at)*F(t)} = f(s-a)…

Q: The linear approximation at x = and where B is: 0 to 1 X is A + Bx where A is:

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Q: Find the linearization L(x)of f(x)at x = a where f(x) = Vx² + 9 at a = –4

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Q: 2: Find the orthogonal trajectories of xy=C.

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Q: ii. Establish the stability estimate for the solution of the problem "() - by(le) + ay(t) + f(4) on…

A: Given that , y''t=byt+ayt+fty''t=abyt+ft Therefore the differential equation , y''t-ab yt-ft=0 The…

Q: a. The function f: RR given by f(x)=x² is twice continuously differentiable in R", and its Hessian…

A: Note: Hi! Thank you for your question. As per the guideline we can solve one question at a time in…

Q: - The antiderivative of f (x) =; whose graph passes through the point (C 3+5sinx+. +3cosx 1(. 5 1(.…

A: Introduction :

Q: 9. f(x.y. z) = In(x + 2y² + 322); P(-1, 2.4): u = -i- j - k

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Q: The function f(z) = 1 has a poles at z = %3| ez – 1

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Q: Find the orthogonal trajectories of the family of x² – y? = cx = CX -

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Q: nake/s the DE nonlinear y' =1-xy+ y2

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Q: d Use the chain rule to calculate f(x) if f(x) In (1+ tº) dt. dx, 0. f(x) =

A: let's use chain rule and find derivative of integral.

Q: If y = x(x – 1)* then y' at z = 2 is equal to

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Q: -2 In(x) Consider the function f(x, y) 3y

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Q: (ii)If y=(x+Jx* +1. prove that y'= Vx +1

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Q: 1 Find F'(0) given that F(x) dt. In(t + 1) 2x

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Q: Find the linear approximation of f(x) = Vx +I at a = 1.

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Q: Suppose that i f(t) dt = x2 - 2x + 1. Find f(x).

A: Consider the following equation: ∫1xftdt=x2-2x+1 fx=ddxx2-2x+1=ddxx2-2ddxx+ddx1=2x-2+0=2x-2

Q: The function f(x, y) = 2xy + yx + 11 has two critical points. Select one: True O False

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Q: Let f(x,y) = 5x² + 6y² + 3xy – 5x – 8y + 36 What is the first coordinate of the critical point?

A: Given data:   The given expression of the function is f(x,y)=5x2+6y2+3xy-5x-8y+36.     Equate the…

Q: Given f (x,y) = 3 – 2x² – 2xy – 2y² – 16x, find and classify all critical points of f. -

A: Calculate fx, fy , fxx , fyy , fxy for f(x,y)=3-2x2-2xy-2y2-16x as follows.…

Q: 13. Prove that the function 2x 1 dt t F(x) is a constant on the interval (0, ∞ )

A: The student has specifically asked for the solution to Question-13. Hence, that question is solved…