Show that the function f: R - {2} (arrow) f: R - {5} defined by f(x) = (5x+1)/(x-2) is a bijection.

Q: Suppose that f(x, y) = at which %3D - {(x, y) | 3 < x < 4, 3 < y < 5}.

A: we have ,  f(x,y)=xy at which (x,y)|3≤x≤4,3≤y≤5 we have to calculate,  ∫∫Df(x,y)dxdy

Q: Show that the function u(z, t) : satisfies ua = %3D %3D a2t2-2

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Q: find the linearization L(x) of ƒ(x) at x = a. ƒ(x) = x3 - 2x + 3, a = 2

A: We find f(x) and f'(x) at x=2

Q: Use the Squeeze Theorem to show that f(x) = x² is in R[0, 3]. %3D

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Q: Find the linearization L(x) at x= a. f(x) = x+ a = - 1

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

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Q: The f(x) 6x2 -5x-4 2x2 +x is discontinuous %3D at x = -1/2. By redefine = w , then f will be…

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Q: Y Show that f (2)= 2+ Con formal maps %3D on %3D

A: Given that,f(z)=z+1zz=1

Q: show that the scalar t that minimizes ||y– tx||

A: In this question, we need to find the t that minimizes ||y-tx||.

Q: 2) Use the Wronskian to show the three functions are linearly independent. f(x) = x, g(x) = cosx,…

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Q: Find the adjoint of F:C3 tends to C3 defined by F(z1, z2, z3)=(2z1+(1-i)z2 , (3+2i)z1 -4iz3 ,…

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Q: find the linearization at x = a. f (x) = x4, a = 1

A: Given function: Using the formula of linearization of a function f(x) at x =a :

Q: Use the comparison theorem with f(x) = = 1 √x to show that [₂²= 1 √x-1 is divergent.

A: See this solution in below

Q: z is a complex variable z=x+iy pic attached with question

A: To analyze and classify the singular points of the given function of the complex variable z

Q: 요2s A) for F- 2K1-3y3+ K %3D prove That divc curl È)=0

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Q: If after evaluating the Wronskian of the functions y1 and y2 the result is W=7x2+19 in the interval…

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Q: Find the linearization L(x) at x = a. 1 f(x) = - x - a = 1 %3D -

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Q: Use Euler’s Theorem to find the degree of homogeneity for f( x1 , x2) = x3 + y3 + 3xy2

A: We will use the Euler's theorem which is : x•fx + y•fy = nf  Where, n = degree of homogeneity    The…

Q: The graph of f(x)= x2 - 1 is concave down on interval | (-1,1) ^O (0,1) BO (-1,0) U (1, ∞ )co (- 00…

A: From the given problem:   fx=xx2-1   As we know that for concave downward:   f''x&lt;0   So,…

Q: Prove that the function : R-{1} →R- {2} defined by 2a f(x)= s bijective. 2 1

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Q: (ii) Verify Cauchy-Goursat theorem for f(z) = 5 sin 2z if C is the square with vertices at 1土も-1土。

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Q: Show that f(x1, x2) = 2 - (x1 - 1)^2 - e^x2^2 is concave.

A: the given function is fx1,x2=2-x1-12-ex22 To find the function is concave we have to show all its…

Q: If f is a function defined from R to R, is given by f(x) = 5x - 3 then f -(x) is given by %3D -- 20…

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Q: Let D, be the linear transformation from C'(a, b] into C[a, b]. Find the preimage of the function.…

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Q: Prove Theorem (AT )T = A

A: Given: Theorem, ATT=A.

Q: Use moment generating functions to show that if X3 = X1 + X2, with X1 X3 - X V3 > vı, and X1 and X2…

A: Solution

Q: 5. Show that the function f (x) has roots between (0,2) x + 2x – 3 f(x) = %3D x – 1

A: Given that: f(x)=x2+2x-3x-1

Q: what is the quadratic polynomial for the function f(x,y) sin(xy) + cos(x/y) at (pie/4, 1) (show…

A: We will find out the required value.

Q: what is the antiderivative F(x) of f(X) = 3x1/2-x-1 that satisfies the condition  F(4)= 0? A,…

A: The given function is fx=3x12-x-1 that satisfies the condition F4=0. Find the antiderivative of Fx.

Q: Let f (x, y) = 4-y² In(y–z²) %3D Draw a picture of the domain of this function.

A: x,y ∈R2

Q: Show that the nth Maclaurin polynomial of f (x) = arcsin x for n odd is 1.3 x Tn (x) = x+ 23…

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Q: Let f (æ) = + and 9(x) = 3 – ya. - 1 and g(x) = 3 – Vx. %3D Find the domain of (gof)(x). (0, 0) (-0,…

A: Now,

Q: b) Show that the function f(x) = x7 +1 is invertible %3D

A: Given that  f(x)=x^7+1

Q: 5. Show that the functions x, x² interval [-1,1]. x are mutually orthogonal in the -

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Q: Show that the function f(x) = x’ + 1 is invertible from R to R.

A: First prove that the  function is one -one  let f(x)=fyx7+1=y7+1x7=y7x=y therefore, the function is…

Q: Find the linearization of ƒ(x) = 2/(1 - x) + saqrt(1 + x) - 3.1 at x = 0

A: Given,

Q: The function on ℤ defined by f(x)=-x^2-5 is onto. True or False ?

A: The given function is                  f(x) =x2-5   Graph:

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: Q1) check the continuity of fX) at X--1, 0,1.2,3 -1<x<1 f(x) = 2x-1, 3x-2 2SxS3 2, 1=3

A: As per the answering guidelines we need to answer only first question so please repost the other…

Q: Compute the subdifferential of f(x): R->R f(x) = x^3 + |x+1| + |2x-1| %3D

A: Solution:Given  f(x)=x3+x+1+2x-1To compute the subdifferential of f(x)

Q: f. Is the domain of f(x,y) = In (3x2 + 3y²) bounded or unbounded? Bounded Unbounded

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Q: Let D, be the linear transformation from C'[a, b] into C[a, b]. Find the preimage of the function.…

A: Dx(f)=8x+5 Apply integration both side  ∫Dx(f)dX=∫(8x+5)dx   f(x)=(8x2)/2 + 5x +c (here c is the…

Q: Find the linearization L(x) of f(x) at x = a. f(x) = a = 0 4x +3

A: topic - linearization of a function

Q: Let f : [0, ∞) → [0, ∞) be the function defined by f(x) = √x. Show that f is a bijection.

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Q: Discuss the continuity in R3 of the function f(x, y, z) %3D x2+ y2+z2 -1

A: Given: f(x,y,z)=1x2+y2+z2-1.

Q: 4. Show that the function f : X → Y defined by f(X) = X U {a} vX €x is a bijection.

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Q: Let f be the function from R to R with f (x) = x2. Is f invertible?

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