Let † : R² → R be the function x2 if (x, y) + (0,0) f (x, y) = x + Y if (x, y) (0,0) By using the definitions only (as limits), compute both f-(0,0) and fy(0,0).

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Q: 9 Prove that if m(x) is differentiable on (-∞, 0) and its derivative m'(x) is bounded then m is…

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Q: Let if (x, y) # (0, 0) f(x, y) = { if (x, y) = (0, 0). (a) Compute the limit as (x, y) → (0, 0) of f…

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Q: H(x) = L, [At) +A-1) ]dt

A: Question derivative of function.

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A: To show that the function f defined by fx, y=1, x, y=1, -1x2+yx+y, x, y≠1, -1is not continuous at 1,…

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Q: Show that the function f defined on [0, 1]'by the conditions 1 f(x)=2rx when 7=1, 2, 3,...... És…

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Q: 2. Determine the points where f is continuous where x + Y if (x, y) # (0,0) f(x, y) = x2 + y2 if (x,…

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Q: 3) Examine the limit of 1 (x² +y²).sin- x*+ (x, y) (0,0) f(x, y) = (0, (x, y)=(0,0)

A: Solution:Givenf(x,y)=x2+y2 sin 1x2+y2To Eamine the limit of a functionFormula:limx→0 sin xx=1

Q: Show that f(z) =xy+iy is everywhere continuous but is not analytic

A: Answer

Q: Show that the function f defined by 1, (x, y) = (1,–1) f(r, y) = { x² + y (x, y) # (1,–1) r+ y is…

A: In this question, the concept of limit is applied. Limit Limits are the points at which a function…

Q: I. Show that the function f defined by 1, (x, y) = (1, –1) f(x, y) = x2 + y (x, y) # (1, –1) x +y is…

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Q: Let f(x) = /20 – x. Compute f'(4) using the limit definition f'(4) - - Find an equation of the…

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Q: Let the function f: R R be differentiable at x = 0. Prove that lim %3D = 0.

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Q: By considering different paths of approach, show that the functions in Exercises 41–48 have no limit…

A: Hey, since there are multiple questions posted, we will answer the first question. If you want any…

Q: Show that the function f defined by 1, (x, y) = (1, – 1) f (x, y) : .2 x + y (x, y) # (1, – 1) x + y…

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Q: Determine if a function f : R2 → R defined by f (x; y) = { x sin(1/x2+y2) , if (x, y) ≠ (0,0) and 0…

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Q: Show that the function f defined on [0, 1] by the conditions 1 f(x)=2rx when 7=1, 2, 3,...... És…

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Q: Find the limit of f(x) as x approaches 2, where

A: fx=1,  x≠20,  x=2

Q: Let f : [0, 1] → [0, 1] be continuous. Show that there exists an element x = [0, 1] such that f(x) =…

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Q: Suppose that f(1) = 5, ƒ(4) = -8, f'(1) = 4, f'(4) = -2, and f" is continuous. Find the value of |…

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Q: Show that the function f defined by 1, f(r, y) = { r2 + y (x, y) = (1, –1) (x, y) # (1, –1) is not…

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Q: 7- Use the limit definition to compute f' (x) and find equation of the tangent line at r = 3. f (z)…

A: topic - derivative of a function using limits

Q: Prove that the limit of xy[(x^2 - y^2)/(x^2 + y^2)] is zero as (x, y) goes to (0,0)

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Q: Let f(x, y) = x2y4 sin(1/ (sqrt(x2+y2)) where (x, y) cannot be (0, 0) and f(0, 0) = 0 Is f…

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Q: Show that the function f(x, y) xy? – 1 has y – 1 no limit as (r, y) → (1, 1).

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Q: Find the Wronskian for the set of functions.{x, −sin x}

A: Given:  f(x1)=x and f(x2)=(-sinx ) The wronskian is given by the following determinant:

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Q: Show that f (x, y) = has no limit as (x, y)→(0,0) Vx2+y2

A: The objective is to show that f(x,y) has no limit as (x,y) approaches to (0,0).

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Q: (a) Assume that f(r, y) is a function given by ry if (x, y) # (0,0), f(r, y) = if (x, y) = (0,0).…

A: We  need to prove the continuity of the function at (0,0).

Q: By considering different paths of approach, show that the functions in Exercises 41–48 have no limit…

A: Hey, since there are multiple questions posted, we will answer the first question. If you want any…

Matrices

‘Matrices’ is the plural form of the word matrix, and it is basically a spreadsheet in the form of a box. In mathematics, various functions can be carried out with matrices. Generally, a matrix comes in the shape of a square or rectangle. The elements are distributed horizontally in the form of rows, and vertically in the form of columns.