Iff: X→Y is an injective function and A, BCX then: f(A-B) f(A)- f(B)

Q: В. B. Show that the function f (z) = -i z2 is analytic.

A: The solution is given as

Q: Find fxx (x,y), fxy(x,y), fyx (x,y), and fyy (x,y) for the function f. f(x,y) = 5x e 8xy fxx (x,y) =…

A:

Q: b) Let f be a differentiable function of one variable, and let z = f(3x² – 5y²). Show that az əz…

A: Given  z = 3x2 - 5y2

Q: Let F(x, y, z) = vy-V %3D (a) Evaluate F(7, 9, 1) (b) Find the domain of

A:

Q: Let f(x) = ax* + bx . If (1,6) is a relative extremum point, then b is? %3D ...

A:

Q: Let f(x) = ax + bx . If (1,6) is a relative extremum point, then b is? %3D

A:

Q: 3 Let fw:2x-y, Find a function y= 9c So that f. 9) (x) = X+ 2.

A: Given f(x)=2x3-4 and f∘g(x)=x+2 We know f∘g(x)=fgx

Q: Find the linearization L(x) of f(x) at x = a. f («) — 4а? + 2а — 3, а — -5 -

A:

Q: hav is that not the function defined by ху f(x, y) √x² + y² if differentiable at (x, y) + (0;0) if…

A: We have to show that f(x,y) is not differentiable at (0,0)

Q: Find fxx (x,y), fxy(x,y), fyx (x,y), and fyy (x,y) for the function f. f(x,y) = 5x e 5xy fxx (x,y)=…

A:

Q: Q.1 A-Find and sketch the natural domain of f(x, y, z) In(2-x2-y2)

A: You have ask multiple  questions  but not specifiy any particular  questions  so , according to…

Q: Consider a function f whose domain is the interval [a, b]. Show that if |f(x) − f(y)| ≤ (x − y)²,…

A:

Q: f(ix, λγ) - λκ. f(x, y)

A: Given: fλx,λy=λkfx,y

Q: Suppose that f(x, y) = e² / y on the domain D = {(x, y) | 0 < y < 2,0 < x < y³}. D

A:

Q: Let f(x, y) = e²x* %3D Evaluate f(3, 5)

A: Given :   f ( x, y) = exy x4   point ( 3,5)

Q: Show that if f (x, y, z) = 0 then = -1.

A:

Q: Let f(x) = ax* + bx . If (1,6) is a relative extremum point, then b is? %3D

A: Given f(x)=ax4+bx

Q: of and ду of Consider the function f(x,y) = 9x' - 4y - 2. Find -

A:

Q: Describe the domain of the function f(x, y) = In(4 – z – y). O {x.y):y<-x+4}

A: Given: fx,y=ln4-x-y Objective of the given problem is to find the domain of the given function. The…

Q: A function f: Z x Z is defined as f(m, n) = 3n - 4m.  Verify whether this function is injective and…

A: f: Z x Z is defined as f(m, n) = 3n - 4m So, f(m, n) = f(a, b) implies, 3n - 4m = 3b - 4a i.e. 3(n…

Q: Find a bijective function f : R^+ → R^+ different from the identity function and has the property f…

A: That's easy. Have a great day!!!

Q: Let f: R² → R be defined by x3 + y3 x2 + y? if (x, y) + (0, 0) f(x, y) : if (x, y) = (0, 0).

A:

Q: Show that the limit of the function f(x,y) = at (0,0) does not exist. (x+y)² x² + y²

A: Limit of a Function: Like a single-variable function, a multi-variable function can also have limit.…

Q: If f is differentiable at xo, prove that f (xo + h) – f (xo – h) – f' (x0) - lim h-0 2h

A: Given that: f is differentiable at xo   To prove: limh→0f(x0+h)-f(x0-h)2h=f'(x0)

Q: 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…

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Q: Let f(x) = be a piecewise function. Evaluate So fo f(x)dx= 3x²+2, 2x - 3, if x < 2 if x ≥ 2

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Q: Consider the function f(x, y) = e-x²-y² defined on the rectangle -2<xs 2, -1 <y < 1.

A: In this question, we find the absolute maxima and minima by using suggested steps.

Q: a) Consider the function f(x, y) = /In (4 – x² – y?). Find the domain and range of f(x, y).

A:

Q: Determine the type of functions from R to R with necessary figure. i) f(x) = 5x + 7 ii) f(x) = (x² +…

A: (i) fx=5x+7 This function is state line and has roots is x=-75

Q: A/ Derive by definition: y = Vx - 3 ? B/ Determine the value of (z) and (k) that makes the function…

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Q: Find fxx(x,y), fxy(x,y), fyx (x,y), and fyy (x,y) for the function f. f(x,y) = 9x e 9xy fxx (x,y)=…

A:

Q: Find and sketch the domain of the function f (x, y) = In(9 – x² – 9y²).

A: The given function,  f(x,y)=ln9-x2-9y2

Q: Let f: R² → R be defined by x3 + y3 x² + y? if (x, y) # (0,0) f (x, y) if (x, y) = (0,0).

A: Given function is f:R2→R defined as  fx,y=x3+y3x2+y2 if x,y≠0,00           if x,y≠0,0. We have to…

Q: 1. Why is f not a function from R to R if a) f(x)= 1/x? b) f(x) = T? c) f(x) =±V(x² + 1)?

A: We'll answer the first question since the exact one was not specified. Please submit a new question…

Q: Let f(x) = ax* + bx . If (1,6) is a relative extremum point, then b is?

A:

Q: Since f(x) is continuous between a and b, the function needs to cross the x-axis. O TRUE O FALSE O…

A: Given fx is continuous between a and b

Q: Determine the antiderivative F of "f" , which is defined by f (x) = 4x3 – 6, where F (0) = 3 %3D

A: Consider the given function fx=4x3-6

Q: Show that the function f : R → R given by f(x) = x3 is injective.

A: To show the given function is injective(one-one), first calculate the value of function at two…

Q: Define f: [0,2]-R by f(x) = x²+2x-1 , then the sup f- inf f is : [0,2] [0,2] .a 3 .b 8 .C 8, .d 1

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Q: Let f(x)= {x^2-8x+16, if x≤3/ax+b if x>3 Find a and b such that the function f(x) is differentiable…

A: Given fx=x2-8x+16x≤3ax+bx&gt;3 is differentiable everywhere so it is also continuous.

Q: O Show that the function f: N2 N defined by f(x, y) = 2X3Y is injective but not surjective.

A:

Q: Find fxx (x,y), fxy(x,y), fyx (x,y), and fyy(x,y) for the function f. f(x,y) = 5x e 5xy fxx (x,y) =…

A: The given function is: f(x,y)=5xe5xy

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).

Q: Consider the function g : Z x Z → Z × Z given by g(x, y) = (x + 3y, 2x y). Is g injective? Proof or…

A: In mathematics, an injective function is a function f that maps distinct elements to distinct…

Q: Suppose that f(x)=xu(x), where u(x) is a differentiable function at x=2 such that u(2)=3, u'(2)=1.…

A:

Q: Let S«) = {r²+2x}°, 121, ax+bx, x< 1. Compute for all a and b such that the function f(x) is…

A: We have to find

Q: Form the PDE by eliminating the arbitrary functions from the relation z = f(xy)

A:

Q: what sets X and Y is the function X Y defined by 3x f (x) = x +4 %3D ijection?

A:

Limits

When it comes to calculus, limits are considered to be a very important topic of discussion. The main importance of limit lies in expressing the value of a function as it gets closer to a certain value. Also, limits can help you to understand other topics, such as continuity and differentiability better. In a broader sense, every calculus notion is a limit. Other branches of calculus have also been derived from limits.