33 Let z=atbi e C with a,belh and i the imaginany unit and define M28= Q -6 a Show that a) Vze C -{o3 : A(1/2) = M(2)-1 B) V2,e C: V22€ C-}o}: M(z./22) = M(2)H(Z2)!

Q: Lut a,bicid by integers such that ad-bc-1. For integes u and y, define Vi u's aut bv and ✓-cut du…

A: Let a,b,c and d be integers such as ad−bc=1. Let u and v be integers and define u'=au+bv and…

Q: 2x-1 Find f1) if Az) = %3D x+2. a) O b) O c) O d) 515

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Q: Sketch the graph of the function and express the function in terms of the unit step function, u.lt).…

A: We will find out the required values.

Q: Q1) Find the canonical form of these question : a) f(x.y,z) =F=x' y' z+x y° z" +x y z b) f(x.y.z)…

A: We are given: f(x,y,z)=F=x'y''z+xy''z''+xyz We are given the standard Form. F=x'y''z+xy''z''+xyz…

Q: VX-2 H Evaluate dy/sx if O y=1X+1)“ Szx-1 at x=\ V(X+3)3 atメ=1 at X-3

A: Reupload other questions according to bartleby guidelines

Q: 20E22. For each pair of Eunctions 'in Exercise 17-34: 9) Find the domain OF f,9, ftg,P-g,fg,F5…

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Q: Show that day) = So, x** 0₁ X=Y. defines a metric on X₂

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Q: find where itin creasing awd deveas ihng also fî hl the alobal maximum and minimam. himan f…

A: Topic- application of derivatives

Q: To evaluate f dx, we choose : ,dv = xdx b)u = Vx - 1, dv = x dx %3D du

A: ∫xx-1dxLet u=x-1.=∫ 2u2+1du=2·∫ u2+1du=2∫ u2du+∫ 1du=2u33+uSubstitute back…

Q: 2yy" = 1 + (y')² 2

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Q: ) Differentiate: Y(u) = (u-2+u-³)(u³ + 3u?) и и

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Q: Prove that i 224 s 2xP for xzO, y zo i and 1 t L-l with p>

A: Given that x,y≥0. And 1p+1q=1 with p>1. Consider gx=xpp+1q-x. Then g'x=xp-1-1 and g'x<0 when…

Q: 0.5(マ+1) 221 if x(z) = x (2) す! (そ-1)(マ-0.6)

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Q: SW= 3, g(2)=. n+3 (iYHow do I find (fo5) (a) and the domain of ) How do I find tgopte (gog)2) and…

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Q: If f(x) = which one of the following is f-¹(x)? a) b) c) x- x-1 2x x d) 2+3 c) = 2 x+2

A: The given function f(x)=xx-1

Q: dx Evaluate LJv by using Trapezoidal rule (up to three 1 + x? decimal places). [Ch-4(B), Expl-2]

A: We have to evaluate ∫01 dx1+x2 by using Trapezoidal rule.

Q: Let T: R3 -> R2 be defined by T(a, b, c) = (a + b, 2a —- c). DescribeT-1(1, 11).

A: T: R3 -> R2 Hence, T-1 : R2 ----> R3 So, necessarily we have to find a, b & c such that…

Q: the second image is not loading?

A: Here we will use the ratio test for convergence of series

Q: az az + x əx %3D Let z = f (x² – y²). Show that y ду

A: The given function is: z=f(x2-y2) Now partially differentiate above with respect to x and y,…

Q: Prove that Vtan a de – 7//2.

A:

Q: Q1 find acubie palonemiat ofk given-points for27,3},(2,12)e

A:

Q: ) Sind dy if : Sincu, u= x

A: As per our guidelines we are suppose to solve only first question if the multiple questions are…

Q: A₁ Let 2 + sinh (2²) - ₁₁ = 27 where w = f (x, y, z)- 1 पुर Find aw дх Jw and Iw > zw. ay dz 3/20

A:

Q: The antiderivative of the function sin (Gx+7) is:

A: Given : sin12x+7

Q: Find the values of af /ax and af lay at the point (4, 5) if f(x,y)=x² + 3xy + y -1

A:

Q: Suppose that Cov(X, Y ) = 5. What is Cov(3X + 4, 9Y )?

A: Cov(X, Y ) = 5 & We have to find Cov(3X + 4, 9Y )

Q: F(t) = A ₁² +B+³ 2 3 t

A:

Q: Vee the definition of the downtie! Find filx) then find fil-2), f'(0), and fi(3) 12 - X 3 b.) f(x) =…

A:

Q: Show that u(x,t)= f((x+a*t)+f(x-a*t))/2

A: Given PDE is utt=a2uxx subject to ux,0=fxutx,0=0 We know that the general solution of the PDE is…

Q: 10. f(x) =-x2 +3x+ m, y 4-IOBI = 10CI %3D A(ABC) = ? B.

A: As per guidelines, we will solve first question poste. 10) Given fx=-x2+3x+m 4OB=OC

Q: Q5:111M) A) Let f: [0,2]R be defined by (3 if xEQ if xeQ fx) = (2) feRn [0,2]. Show that (1) / is…

A: This question is related to limit and continuity .solve in step 2.

Q: Determine whether f is a function from Z to R if a) f(n) = tn. b) f(n)=√√n² + 1. c) f(n) = 1/(n² —…

A: Function: Let f:M→N be a function, then every element of set M has one and only one image in set N.

Q: Lemma*: If z(x, y) = W+H, then xZx + y2y = (xWx+yWy) + (xHx + yHy).

A: Solution: