7. Suppose f(x) = ax+b/cx−a ,for real numbers a, b, c with both a and c not zero. (a) Find the domain of f. (b) Find a condition on a, b and c which guarantees f(f(x)) = x for all x in the domain of f.

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

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Q: 0 0 0 1 0 0 0 1 0 ) Let A =

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Q: 1- Prove the following relations: ag = (x – t) g(x, t) at (1 – 2xt + t?)- (1) (1 – 2xt + t?) ag = t…

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Q: Then, the only positive equilibrium point of Eq.(1.1) is given by (2.7) (1 – A) (E Bi) Li=1 provided…

A: Given linearized equation of Eq(1.1) about y~ takes the form ;…

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

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A: “Since you have asked multiple question, we will solve the first question for you. If you want any…

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: t2 and y2 3 are two distinct solutions of the IVP t²y" – 4ty + 6y = 0, The functions yi %3D y(0) =…

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Q: 29. In Theorem 9.8, if f'(x o) = 0, no conclusion can be drawn about the equilibrium point xo of x'…

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Q: 15.4.59 Assume that F(x.y,z(x,y))3D 0 implicitly defines z as a for xyz + 8x + - 4z = 0. dz

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Q: manufacturing company employs two devices to inspect output for quality control purposes. The first…

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Q: Find ther critical point x* of 2 f(x)=312921 22 −5+1 73 +7x₂² +372 73 +6x3² − 3x₁ +3x₂ + 3xg +8…

A: As per the question we are given a quadratic multivariate function f(x) And a constraint g(x) = -8…

Q: Let y : R →R be the real-valued function defined on the real line, which is the solution of the…

A: Ans:-  Initial value problem: y'=-xy+x,  y=0=2          solution : y'+xy=x, 40=2          is of…

Q: 1) A course repeater claims that his brother who did some Calculus at college years ago, but…

A: (1) ⇒f(x)=(2x2-1)(x2+3)x2+1⇒f'(x)=(x2+1)ddx(2x2-1)(x2+3)-(2x2-1)(x2+3)ddx(x2+1)(x2+1)2    (∵using…

Q: *) Use the Wronskian to determine whether the functions y₁ = sin(3x) and y₂ = cos(4x) cos(4x) are…

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Q: An ODE is said to be stable is every arbitrary constant on its solution, such as C1 and C2 for…

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Q: The Wronskian 1. Show that the functions ex, cos x and sin x are linearly independent.

A: As per guidelines, We’ll answer the first question since the exact one wasn’t specified. Please…

Q: 2. Show that 4=x i+y°j+:'k is irotational.

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Q: 1. A function f(x, y) is homogeneous of degree 7 in x and y if and only if, 2. The function f(x, y)=…

A: We have to find degree of homogeneous function

Q: 10 a- Let X1, X2, ..,Xn~N(0,0) and T Find %3D X2 E (T),Var (T)

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Q: Prove that for the gamma function [(x) = ftx-¹e-tdt that for n a positive integer then I(n) = (n-1)!

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Q: (8) Suppose f(x, y) = -x + y², x = s² +t°, y = 2s – 3t. Compute f, when s = 1 and t =-1. %3D

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Q: If the Wronskian of the three functions ex v is equal to zero, then the function y satisfies the DE…

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Q: Given f(x)=6*x^3+6*x^2+-4*x, identify the two critical values. Put the most positive critical value…

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Q: 1 1 Prove that: L' a exp(a't) erfe( avt), where erfc is complementary a+v error function.

A: Formula Used:- L1t=πsLeat=1s-aLerf(at)=as(s+a)Leatf(t)=F(s-a)                   where…

Q: 1+ By using the definition In(1+x) = / 1 -dt, show that for a certain range of values of r, t…

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Q: 1 1 Select all the antiderivatives of f(x)=-+ %3D x² +1

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Q: 9- The general solution for the PDE (DD, + D,D-12D =0 is a. u(x, y) = G,(x)+G,(x+y)+G,(x-y) b. u(x,…

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Q: Differentiate. 11. f(x) = e* %3D 12. (x) = e* 13. g(x) = e2x 14. g(x) = ex 15. f(x) = 6e* 16. /(х)…

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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. Let flxx) = x³ + y3 - 3x2-3y2 - 9y. (a) Find all of the critical points of f.

A: Part (a): (i) Find derivative of x and y. (ii) Equate to zero, to get critical points.

Q: Evaluate: √x(x - 5)dx Solution: √ √x(x - 5) dx = f x²(x - 5) dx by law of exponents/ = f (x² - 5x)…

A: Given problem:- ∫√x(x-5) dx

Q: Determine the GINI Index of Country X whose Lorenz curve is f(x) =;x² +÷x*. If Country Z 3 has a…

A: The Lorenz curve  of country X is f(x)=12x2+12x4. The GINI index  of a certain country with Lorenz…

Q: 15. Let f(x) = x² -4x+3. What are the critical number(s)? x = 1 b. x = 3 c. x= 1 and x 3 a. d. x = 2…

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Q: One of the critical points of f (x,y) = x3 - 5y2 + 10y-27x is: O (1,-1) O (3,1) None of these O…

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Q: 4.8. Show that Dirichlet's function 1, if x is a rational number, { otherwise f(x) = 0, is not of a…

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Q: 1. Prove that for all x, y ER, max (x, y) x+y+lx-yl 2 x+y-lx-yl 2 and min (x, y)=-

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Q: Expand xy² + 2x – 3y in powers of (x + 2) and (y – 1) upto third degree | terms.

A: Given ,  f(x,y) = xy2 + 2x - 3y  By Taylor's theorem  f(x,y) = f(a,b) + {(x-a)fx(a,b) +…

Q: The critical Points of f(x, y) - x' -3x +3y2-6y are: None of these O (1,1) and (-1,1). O (01) and…

A: We will find the first order partial derivatives of f and equate them to 0 to find the critical…

Q: 12. Find the general solution using Reduction of Order: a) y" = In x

A: you have asked multiple questions in a single request we would be answering only the first question…

Q: Consider the following NLP problem: f(æ) = -x+ 2x1 – 122 – T2 +1 max s.t. I2 > 1. Determine if x =…

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Q: 4. Decompose into f(x) and g(x) such that h(x) = f(g(x)). %3D (a) h(x) = (3x + 2)² f(x) =_ g(x) =,…

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Q: 2. If the Wronskian of y1 and y2 is e2" (x² + 5) and y1 = e2", find y2. %3D

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Q: The critical Points of f (x, y) = x³ - 3x +3y2 -6y are: O (-1,1) and (1,1) O (1,1) and (1,1) O None…

A: It is given that, f(x, y)=x3-3x+3y2-6y   Critical points of 2 variable function are the point where…

Q: 7] The Wronskian of the functions 1, x, and e -2x is (а) е' -2x (2x+1) (b) 4e-2x (c) -e(2x +1) (d)…

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Q: If the functions f(x², y²) and g(x, y) are homogeneous of degree 2 and 4, f (x, y) g(x, y) 1…

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Q: 1. A force of F (x) 2x = xe + 6x – 2 acts on an object. What is the work required to move the object…

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

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Q: If f" (c) > 0 where c is a critical number of f' (x), then (c, f (c)) is a relative maximum of of f…

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Q: x2/3 is (are) The critical number(s) of f(x x – 1

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Q: min ||y – Hx|3 + A ||x||3 x = (H'H + AI)-1H'y (18) In reference to (18), why is HTH+ AI with A > 0…

A: Given - minx y - Hx22 + λx22 ⇒ x = HTH + λI-1HTy           18 To find - In reference to (18), why is…

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