5. Let f and g be two invertible functions. Prove that (a) (f o g) is an invertible function, and (b) (f o g)¯'(x) = (g¬1 o f-1)(x).

Q: 1 Let f (x,y) =In Then f (1, – 1) =... 3x2+4y3 XX

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Q: 22 dt at x = 4. ind the linearization of f(x) = 7 - 4 +t

A: Consider the given function fx=7-∫7x+3224+tdt

Q: Example H·W: for f(x,y) = cos(xy) - x3 + y compute fxyy, fxxyy

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Q: 2. If :|S1, determine the maximum modulus f(:) (a) f(=) =z-2z+3, (b) f(=) == +z-1, (c) f(=)3= :+1…

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Q: 2. Determine whether the functions f1(x) = e2", f2(x) = e=2#, and f3(x) = sinh 2x are linearly…

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Q: 3. (a) Show all functions satisfying u"(x) = 0 are linear by integrating the expression of u"(x) %3D…

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Q: (a) Find if y = y (ln r). (b) The function f(z) (In r) is an invertible function (you do not need to…

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Q: 2x* + ax + b Part A: Consider the function f defined over]-0; 2[ U]2;+«[ as : f (x)= where a x- 2…

A: Given data: The given function is f(x)=(2x2+ax+b)/(x-2). (a) The expression for the derivative of…

Q: du -xy du Ifu =f(x² +2yz,y² +2zx) Prove that (y- zx)-(x² - yz) -NX ду

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Q: If f (x) is an invertible, differentiable function with tangent line y = 4 x + 7 at the point (0, 7)…

A: we have to swap variable for finding the inverse function

Q: 1. Show (in terms of e – 6) that a function f : [2, 7] → R be defined by f(x) = Vx² + 1 is uniformly…

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Q: 6. Consider the function f(x, y) = cot ¹(1+x) — 2e¹+³y If x = s²-t² and y = 3t+tan(1-s), use the…

A: Let's evaluate given partial derivative.

Q: Find dy/dx for f(x) = (Inx)x^2 b)Function f(x) = (Inx)x^2 is an invertible function. Please compute…

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Q: Find the local linearization of f(x)=x^(2) at 2

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Q: Find the linearization L(x) of f(x) = cot(x) at x = π/4.

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Q: Let g(x, y) = x4 + y² – 4x³ + 5x – 6y+3. Show that g(x,y) continuous (actually at least aC')…

A: Recall [ Implicit Function Theorem ]

Q: Let f (x,y) =In Then f „(1, – 1) =... 3x²+ 4y3

A: This is a problem of partial.

Q: Let z be defined implicitly as a function of x and y by the e e-zy əz find O UTM + cos (xy) = (4 –…

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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: Show (in terms of e - 6) that a function f : [2,7] R be defined by f(z) = V² +1 is uniformly…

A: In this question, we need to show the given function f(x) is uniformly continuous.…

Q: If Σ α An diverges then E ca can diverges only if c > 0 only if c < 0 only if c+ 0 for any real…

A: Given, ∑an diverges then find for which values of c, ∑can diverges.

Q: ) Find the linearization of f(x) = sinx at x = 0.(b) Compute dy if y = x2 +x and x changes from x =…

A: Since you have submitted two questions, we'll answer the first question. For the second question…

Q: If Σ An diverges then > can diverges O only if c>0 O only if c< 0 O only if c+0 O for any real value…

A: Given, the series ∑an diverges, then we have to find the values of c for which the series ∑can…

Q: 1. Determine whether the functions f1(x) = cos 3x, f2(x) = x, and f3(x) = cos² x are linearly…

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Q: Verify Young's Theorem In(2x + y) y2 x2 + + e(x+2y)

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Q: 1. Show (in terms of e – 8) that a function f : R³ → R defined by f (x, y, z) = (2x + 3y + 4z) is…

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Q: 11. The function f(x) is defined on [1, o0) and satisfies VTO dt. 10 Find f(x).

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Q: [1] Show that the functions In x, In(x) are linearly dependent on (0, co)..

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Q: 11. Show that the Beta function, defined by B(x,y) = (1-t"-1 dt , for x> 0, y > 0, satisfies the…

A: the given function is βx,y=∫01tx-11-ty-1dt for x&gt;0,y&gt;0 substitute t=1-s therefore, dt=-ds when…

Q: 1. (a) Let f(r,y)- cos(z + 2y). Compute the diectional derivative Df(r,9), where u- (b) Compute ff,…

A: Solve the following

Q: (b)Assume that f(x) is a function of the form -x-1; when -T < x <0 f(r) = when 0 <r < T Prove…

A: For the solution of the problem follow the next step.

Q: 2. Suppose that f is a twice differentiable function (everywhere). The so-called arclength kernel of…

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Q: Find the linearization L(x) of f(x) = cot x at x = 4

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Q: Find the linearization of the function f (x)= x³ at x = 1. qb |a| sin (a) L (x) = Using this…

A: Given, fx=x5 We know that, If we have a differentiable function f defined near "a" the linearization…

Q: 25. The function g(x) = [", |u| du is not differentiable at x = 0.

A:

Q: 1. Integrate the function f(x, y) = x – y over the triangle T with vertices (0,0), (1,0), and (1,2).

A: Given triangular region is bound by the vertices 0,0, 1,0 and 1,2. The sides of the given triangular…

Q: Suppose fn → f and the functions fn all satisfy the Lipschit condition |fn(x) – fn(y)| < Mx – y| for…

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Q: д. L. = a(x, y)+b(x, y) +c(x, y). – d(x, y) -

A: Proof: Consider V be any vector space of all functions of two variable x  and y whose partial…

Q: Example H-W:_for f(x,y) = cos(xy) – x³ + y* compute fxyy, fxxyy %3D

A: We have to find the partial derivative

Q: ) Consider the function f(r) = f(1) has a critical number A %3D f"(A) = Thus we conclude that f(x)…

A: Critical point f(x) is the number at which first derivative is zero.…

Q: 7. a) Show that F(x,y)= is a conservative field. b) Find a potential function ø(x, y) fa [show your…

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Q: 5 The function f(x, y) = | x' cos is homogenous inx and y of degree

A: Given that: f(x, y)=x2cos2yx-y2+x3y

Q: 2. Show that fxy and fyx are equal for the function f(x, y) = x²y sin(x + y). %3D xy. cos(xry) + 2xy…

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Q: 1 Let f (x,y)=In . Then f „(1, – 1) =...... 3x²+4y3 XX

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Q: Let L(r) be the linearization of f(x) = sin x + 1 at the point x = . Find L(π/2).

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Q: Find the linearization L(x) of the function at a. f(x) = sin(x), a = %3D L(x) = %3D

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Q: 14. Use the Cauchy-Riemann Equations to show that f'(z) does not exist at any point. f(2) = Z b)…

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Q: Show that the functions ƒ 1 (x) = sin x, ƒ 2(x) : = cos x, and f 3(x)=x cos x are linearly…

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Q: 2. Let f(t) be a continuous function on the interval [0, 27]. Suppose the 1st order Fourier…

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Linear Algebra

In mathematics, problems can be solved by the arithmetic operators like addition, subtraction, multiplication, and division. In algebra, we represent the numbers by any letter called a variable. If these variables are of degree 1, then it is studied under linear algebra. The first-degree equations involving algebraic expressions are called linear equations. That is, if you represent it by drawing a graph you will get a straight line.