omot rix over the field F& roo- Every equitha lemt to mx n veduced metoix.

Q: Find the area of theregion-thatis bqunded by the girencove and lles m the speafICd SECAET 2.

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Q: OProve that (r=s)Er S is toutology?

A: The objective is to prove that r≡S≡r↔S is a tautology.

Q: a²z If z = In(x² + y²)., find ax2 ay?

A: Here we have;  z=ln(x2+y2) ...................(1) partial derivative with respect to x

Q: Show that if fis adifferentiable function, then Z:xf()Satis fies そ

A: Partial derivative and derivation

Q: A counterexample can be used to prove a theorem is false. O True O False

A: We have to check

Q: Under a change of variables z = u°/3, y = v²/2 , the infinitesimal element of area dædy becomes 6uv…

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Q: Let r ERQ. Prove that for all a, b, c EQ, =cr iff a = 0 and b = c. a + br

A: Given that r∈RQ Let a,b,c∈Qa+br=cr iff a=0 and b=c

Q: Prove that OfVg.dr = ] (Vfx Vg) · N ds.

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Q: cothiz-l=eschz

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Q: 3y², Compute divà and curlà for à = (x²y²z?)î – (2xy² – 16x)ĵ + (9_)&.

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Q: that uni, o wthat (h) 3.

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Q: O) Lind dyldx of 3 xex 1o X +3y = 0 2sinx cos y =1 9 x = sec 'y (2)

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Q: xy W=Ze y=8+tZ-St (Hiw) at

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Q: let 19, b) = 1, them prove that there exists x20 Such that ijzo ax_by = 1

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Q: Evaluate tne below exprassion using De Moivres meorem-

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Q: 1.A=32 find &. 12. Finda, pOsitive and cotermal!volue negatives for T

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Q: Q1: Find all the ichempoten! element of the xing 25 nilpoten t

A: