makaut-bs-m-102-mathematics-1b

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Sayani saha

Asked: February 4, 2021In: MAKAUT

11(c) Find the directional derivative of f= xyz at ( 1, 1, 1 )in the direction $2{\mathop{i}\limits^{\wedge}-{\mathop{j}\limits^{\wedge}-2{\mathop{k}\limits^{\wedge}$ .

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0

Sayani saha

Asked: February 4, 2021In: MAKAUT

11(b). If y=tan $^{-1}$ x then prove that

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i) (1+ = 1 ii)

0

Sayani saha

Asked: February 4, 2021In: MAKAUT

10(b). Find the evolute of the ellipse $\frac{{x}^{2}}{{a}^{2}}+\frac{{y}^{2}}{{b}^{2}}$ =1.

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0

Sayani saha

Asked: February 4, 2021In: MAKAUT

9(c).Using Parseval’s identity corresponding to the Half-Range cosine series of the function f( x )= x, 0 < x < 2, find the sum of the series

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*** QuickLaTeX cannot compile formula: (\frac{1}{1^{4} + {1}{3^{4} + {1}{5^{4}) *** Error message: File ended while scanning use of \frac . Emergency stop. +…..

0

Sayani saha

Asked: February 4, 2021In: MAKAUT

9(a). Show that the rectangle of maximum area that can be inscribed in circle is a square.

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0

Sayani saha

Asked: February 4, 2021In: MAKAUT

8(c). Use Mean-Value theorem to prove the following inequality $\frac{x}{1+x} < log( 1+x )$ $<x, \text{if} \; x<0$ .

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0

Sayani saha

Asked: February 4, 2021In: MAKAUT

8(a).Find the angle between the surface $x^{2}+y^{2}+z^{2}=9$ and $x^{2}+y^{2}-3=z$ at the point ( 2, -1, 2).

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0

Sayani saha

Asked: February 4, 2021In: MAKAUT

7(c). Check the consistency of the given system of equations and solve if possible :

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x + 2y – z = 10; x – y – 2z = -2; 2x + y – 3z = 8.

0

Sayani saha

Asked: February 4, 2021In: MAKAUT

6. If $f=x^{2}y + 2xy+z^{2}$ , then show that curl grad $f$ = 0.

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0

Sayani saha

Asked: February 4, 2021In: MAKAUT

5. Find the maximum value of $x^{3}y^{2}$ subject to the constraint x + y = 1 , using the method of Langrange’s multiplier.

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11(c) Find the directional derivative of f= xyz at ( 1, 1, 1 )in the direction $2{\mathop{i}\limits^{\wedge}-{\mathop{j}\limits^{\wedge}-2{\mathop{k}\limits^{\wedge}$ .

11(b). If y=tan $^{-1}$ x then prove that

10(b). Find the evolute of the ellipse $\frac{{x}^{2}}{{a}^{2}}+\frac{{y}^{2}}{{b}^{2}}$ =1.

9(c).Using Parseval’s identity corresponding to the Half-Range cosine series of the function f( x )= x, 0 < x < 2, find the sum of the series

9(a). Show that the rectangle of maximum area that can be inscribed in circle is a square.

8(c). Use Mean-Value theorem to prove the following inequality $\frac{x}{1+x} < log( 1+x )$ $<x, \text{if} \; x<0$ .

8(a).Find the angle between the surface $x^{2}+y^{2}+z^{2}=9$ and $x^{2}+y^{2}-3=z$ at the point ( 2, -1, 2).

7(c). Check the consistency of the given system of equations and solve if possible :

6. If $f=x^{2}y + 2xy+z^{2}$ , then show that curl grad $f$ = 0.

5. Find the maximum value of $x^{3}y^{2}$ subject to the constraint x + y = 1 , using the method of Langrange’s multiplier.

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