1. Let f (-1,1) R, f(x) = (1+x³3)-3. Compute g': (0,1) → R where : (a) g(x) = få ƒ. 0 (b) g(x) = [ x f. f.

Q: 3. Find the fixed point(s) of f : [1, 0) → [2, 0) defined by f(x) = vx² + x.

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Q: Show that the function f(z)= Im(z) is nowhere differentiable.

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Q: 1. Find the most general antiderivative or indefinite integral for the function. (Ilint: Using a…

A: to find integration.

Q: Q3) If f(z) is analytic function and u(x, y) = x3 – 3xy find f(z)

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Q: Find y as a function of x if x²y" +5xy - 12y = x², y(1) = −9, y(1) = 9. y=

A: We have to find as a function of .

Q: 3. (b) Consider the function f(x, y) = a(x² + y²) + xy + 1 for some real number a. Find Vf. Find fxx…

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Q: √x² + y² x-1 (a) Find and sketch the domain of f (x, y). 2. Consider the function f (x, y) = 4 (b)…

A: The given function is  f(x,y)= x2 +y2-4x-1 We know that the domain of a function is the set of…

Q: Suppose that y is a function of u, u is a function of x, and u = -1 when x = 2. If du/dx|x=2 = 3 and…

A: Solution

Q: a) Differentiate the function Q(p) = -2√/p³ (e-P-PB). b) Hence or otherwise, determine Q'(1).

A: The given function .The aim is to find the derivative function  and find the value of .

Q: Use the table to determine Df(g(x))) at x = 3. |1 2 3 4 f(x) 1 f(x) |3 -5 1 4 4 1 3 4 3 2 g(x) 2…

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Q: . Show that the function f: R→ R defined as f(x) = 13x − 15 is one-to-one.

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Q: Let f(x) = x – 5, g(x) = /x , h(x) = x°, and j(x) = 3x. Express each of the functions given below as…

A: The solution of above question is written in below steps.

Q: Let f(x, y) = 3x² + 4y? – axy. (a) Find the values of a such that the graph of f increases when…

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Q: 1. Let f : (−1,1) → R, f(x) = (1+x³)-³. Compute g' : (0, 1) → R where (a) g(x) = X X f. (b) g(x) =…

A: Answers along with explanations are provided in the image. Explanation:

Q: If f(z) is analytic function and u(x,y) = x3 - 3xy find f(z) %3D

A: Given that the real part of the analytic function f(z) is, u(x,y) =x3-3xy To find the analytic…

Q: 4. Find the functions f(x), g(x),h(x) that satisfy: f(g(h(x))) = 2.

A: A composite function is created when one function is substituted into another function .

Q: 2. Let f= L(X,Y). Show that ƒ is one to one iff (f(x).(x)....(x)) is linear independent when (x,x)…

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Q: 5) Find functions f and g so that f • g = H -3 H(x) = Vх — 2

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Q: The function, f(x), in the graph below has f(1) = 1 and f'(1) = 2. Which of the following are the…

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Q: B. Find and classify the extreme points of function f(x, y) = x + y - 4xy-1.

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Q: Compute f(s), where f(z) = e and 8

A: The given function is  and

Q: Find y as a function of a if y(1)=2, y(1) = 1. y = r²y" + 7xy +9y = 25,

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Q: Q3) If f(z) is analytic function and u(x, y) = x - 3xy find f(z) |

A: We have to find analytic function using C-R equation.

Q: 2. Determine f'(-1) for the function f(æ) = (x" – 2r° + 1)(x³ + æ -- 2). 8 (B) 12 (C) 14 (D) -4 (E)…

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Q: Let f(x) be defined by f(x) = 3x² + 5x – 40. Let (a, b) be the point on the curve y = f(x) such that…

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