) Let (x, y) €Rx R. Consider the following functions from R2 to R? r(x, y)) = (-y,x) and s(x, y) = (x,-y). (a) What is the order of r? of s? Justify. Note: r" = rororo..or. n times (b) Let f be of the form r's' where 0 s is Ir| and 0 sjs Isl. Fill in the table with these distinct funct and their images. image of (x, y) f i (x, y) (-y, x) (x,-y) It may be nice to enumerate the elements alphabetically, e.g. list rs ahead of r's. (c) Draw the point P(x, y) on quadrant I of the real plane. Show the image of P under each function f ex for the identity i. (d) The set K = {rs' | 0sis Ir| and osjs Isl } is a group. Construct the complete group table for K

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A: f:ℝ2→ℝ and g: ℝ2→ℝ f is C2 Hf4,5=2-1-13 g is defined by gx,y=fx-y,yx

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Q: 10e? dz by residue theorem, where C'is the contour z| = 2 1:4 + 52ª Evaluate

A: Complex integration

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A: By substitution, we calculate the following Integral.

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A: We can use the limit in order to proof the continuaty at that point.

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Q: Given the function f(x,y)=- 4y? find each of the following. SIMPLIFY A) f,(x,y) =, %3D B) f,(x, y)…

A: Power role of derivative: ddxxn=nxn-1 Derivative of function eax: ddx(eax)=aeax Given function is…

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Q: 3. Which function has a range of yS 3? Ax) -- +3 с. a.

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A: Topic-complex number

Q: For the function f)=5. find fx)

A: substitute the given function as equal to y and find value of x in terms of y

Q: 10) s) =-2 -2

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Q: let (Riae) be aring of real numbar's andf fg Eply R. Such That f= to,,-1,22010-) F-lo-してソの (hoラ-20 )…

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Q: las For the folowing bunction f(u) - 2)c? -3jc +3 2)c' -3jc %3D n'-qut2 which Irunction O Find Hhe…

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A: We have to prove the given statement.

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Q: 04 Let f(x) be a contineous function such that Ler - 5/W)dx = = 4 and =9, then a) 81 b) 101

A: Use definite integration property

Q: B/let Flx)=[X]-X,x E(-2,2).which valuesof x o E(X) continuaus?

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