(a) , f(r cos 0,r sin 0 )rdrde

Q: If z = cos (x + ay) + sin (x - ay), with a ∈ R, then the result of a(∂z/∂x) + (∂z/∂y) corresponds…

A: If z = cos (x + ay) + sin (x - ay), with a ∈ R, then the result of a(∂z/∂x) + (∂z/∂y) corresponds…

Q: sin (t) -dt 3 (4+ cos (t))?

A:

Q: 19.Show that W[eλt cos(μt), eλt sin(μt)] = μe2λt.

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Q: Two waves travelling in the same directio are given by: y1 = 0.2 sin(2ttx-20t+0) and

A: Given,  two waves travilling in the direction are                     y1=0.2sin(2πx-20t+φ)…

Q: Compute -i + cos -i sin a - sin a + i cos a where a E (T, ).

A:

Q: IER, t> 0, u(x,0) sin(87r) cos(90z). u + ru, =x

A: Solve partial differential equation by Lagrange method. Rewriting partial differential equation…

Q: b. Show that 0s cos ay dA s where R= (0. G ) sin Ax

A: This is a problem of double integration and inequality.

Q: Show that both y = sin x and y = cos x satisfy y" = -y.

A:

Q: cos z dz (4 + sin z)?

A: The solution of above integral is written in below steps.

Q: 4 sin' t cos tdt 4 sin"(t) cos (t) %3D

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Q: f(1, y) = cos cos y is = COS I COS y

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Q: 2 sin(t) s(t) = et

A: Part (a) The displacement of the object is, s(t)=2sintet Integrate the expression with respect to t…

Q: + b¬ + cx = 0 dt lution given by: - (A sin ßx + B cos ß.

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Q: // Show that y" + y = 0, given that y = 2 sin x + 3 cosx

A: First find the first and second derivative of the given function then simply put and simplyfy

Q: Show that y" + y = 0, given that y = 2 sin x + 3 cosx

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Q: y = cos(2x), y = sin x, 0<x< 2

A: Solution is given below:

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Q: If x = sin2 (u) and y = cos² (u), then dy is : dx а. 1 b. cot(x) C. tan(x) d. 1-

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Q: Prove that: cos(nx) - cos(na) cos(x) – cos(a) sin(na) sin(a) dx = n neN, a ER - {0}

A: To solve this question take different values of n and calculate LHS and RHS separately.     if…

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Q: Show that y / / + y = 0 given that y = 2 sin x + 3 cosx

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Q: If S sin 2y cos 2y dy = =, then x is equal to: %3D

A: Hint:    sin2θ=2sinθcosθ

Q: Use an appropriate local linear approximation to estimate the value of cos(29°). cos(29°) -

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Q: Let I = 3x*cos (x) dx. The approximation of / using the two- formula is:

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Q: 6) F Sin12y Cos’ y dy

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Q: (3 cos t – 1)i + (2 sin t + 3)j,

A: We sketch the curve as

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Q: Suppose f(x, y) = x2 + y? where x = r cos 0 and y = r sin 0. af and Or 1, 0 = 6 Find -when r

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Q: O sin (z)cos(z)dz

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Q: A particle moves in the xy-plane so that its position at any time t is given by x= cos(5t) and y =…

A: According to the questionx=cos5ty=t3

Q: ) // Show that y + y = 0, given that y = 2 sin x + 3 cos.x

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Q: Given f(x,y) = e X cos y, Evaluate fx(0,2) cos 2 -sin 2

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Q: (2 cos t, 2 sin t, t), where 0 <t < .

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Q: Given f(x,y,z) = cos(5xy) + sin(4z). Find fx(6,6,0). Leave your answer correct to two decimal…

A: Given f(x,y,z) = cos(5xy) + sin(42). Find fx(6,6,0)

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Q: I sin(z) cos(z) da : Hint:

A: Given integration is, ∫xsin(x)cos(x)dx We know that, 2sin(x)cos(x)=sin(2x) Now, the integration…

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Q: 2. Prove that, V{(sec 0 - 1)/(sec 0 + 1)} cot 0. = cosec e

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Q: If x=sin8,y=0 ,y=cosp0,Prove that (1-x') y,-xy,+p°y=0 where y2 d'y dy and y,- dx? dx

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Q: Prove that d/dx [cos x] = −sin x.

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Q: a sin a + In v ) da + tan adv = 0 Cos a

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Q: sin?x d Prove that 2sinx dx \(1+cosx)² (1+cosx)²

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Q: dy is let y = cos(In(cos(x))), then da

A: Hey, since there are multiple questions posted, we will answer first question. If you want any…

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Minimization

In mathematics, traditional optimization problems are typically expressed in terms of minimization. When we talk about minimizing or maximizing a function, we refer to the maximum and minimum possible values of that function. This can be expressed in terms of global or local range. The definition of minimization in the thesaurus is the process of reducing something to a small amount, value, or position. Minimization (noun) is an instance of belittling or disparagement.

Maxima and Minima

The extreme points of a function are the maximum and the minimum points of the function. A maximum is attained when the function takes the maximum value and a minimum is attained when the function takes the minimum value.

Derivatives

A derivative means a change. Geometrically it can be represented as a line with some steepness. Imagine climbing a mountain which is very steep and 500 meters high. Is it easier to climb? Definitely not! Suppose walking on the road for 500 meters. Which one would be easier? Walking on the road would be much easier than climbing a mountain.  

Concavity

In calculus, concavity is a descriptor of mathematics that tells about the shape of the graph. It is the parameter that helps to estimate the maximum and minimum value of any of the functions and the concave nature using the graphical method. We use the first derivative test and second derivative test to understand the concave behavior of the function.