P5: nts) Assume that f is a function such that fæy and fy exist and are continuous. Assume additionally that f(tx, ty) = t™ f(x, y). for all numbers x, y, and t. Show that x202f ?x2 8² f əxəy 20² f дуг Hint: Differentiate twice with respect to t. Then take t = 1. + 2xy- +y²5 - m(m − 1)f(x, y)

Q: 73-74 Find the distance between the given parallel planes. 73. 2x - 3y + z = 4, 4x - 6y + 2z = 3

A: Solution:

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Q: Given the polar function: r = 1-2sin (0) What is the area in the small loop? ?] square units

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Q: a. Show that n(t)= -g'(t)i + f'(t)j and - n(t)=g'(t)i-f'(t)j are both normal to the curve r(t)=f(t)i…

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Q: Prove that quadrilateral ABCD,where AB≡ x+y-10 ,BC≡x-7y+50=0 ,CD≡22x-4y+125=0 and DA≡2x-4y-5=0  is…

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Q: If H is a Hilbert space and SCH, show that S = S¹¹¹. When S is the same as S++ ? Justify.

A: Answer:If H is Hilbert space and SCH, show that S⊥=S⊥⊥⊥.when  S is same as S⊥⊥? Justfy.These…

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Q: (a) Find the determinant of the following matrix. A = -202 0 1 0 -3 03 4 101 0 2 1

A: A=-2020210-310341010 Note: We are allowed to solve 1 question at a time.

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Q: Question 5 Solve the exact differential equation (-5 sin(x) -y sin(x) + 3 cos(x))dx + (cos(x))dy = 0…

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Q: educe the line 2x-3y+5=0 in slope intercept,intercept,and normal forms.

A: We have             y=2x3+53≡mx+c  ←Genernal Equation of line  tanθ=m=23,c=53

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Q: a.) 4xy" +3x³y'-7x = sin(2x)e²x dy dx b.) 5xy+3 = 2e¹¹ N

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