Find the -of the following function : ду w = cos (x2 + 2 y) – e4x- z*y + y3 .A a w = 2 sin ( x2 + 2 ) + e4x-z*y + 3 y? ду .B a w = - 2 cos ( x2 + 2 y ) + e4x-z*y + 3 y? a y .C sin ( x2 + 2 ) + z* e4x-z*y + 3 y2 a y .D -=- 2 sin (x2 + 2 y ) + z4 e4x-z*y + 3 y? ду

Q: 3. Differentiate. SET A. y = 3 cos(5x2 + 2)

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Q: 2. If f(x, y)=x² sin y-y cos.x-xe - ye" +5x°y°, show that ô²f _ ô²ƒ ôxôy ôyôx

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Q: Let ro)-플-x a-글 FW) = b = 0, and n=3. Then: cos (f(x))dx =

A: We can find the integration as below

Q: Consider the following IVP: y" +y' = -cos x; y(0) = a, y'(0) = b Find the general solution. A y(x) =…

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Q: 2. If f(x, y)=x² cos y-y' sin x-xe'-ye* +2x*y', show that ôxôy ôyôx

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Q: Find the Wronskian for the set of functions.{1, sin 2x, cos 2x}

A: Here the given function  {1, sin 2x, cos 2x}

Q: Suppose that f(π/2)=−3  and f′(π/2)=8 and let g(x)=f(x)sinx and h(x)=(cosx)/(f(x))  Find h′(π/2)

A: Given that f(π/2)=−3  and f′(π/2)=8 and let g(x)=f(x)sinx and h(x)=(cosx)/(f(x))

Q: Consider the following IVP: y +y = -cos x; y(0) = a, y'(0) = b Find the general solution. A y(x) =…

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Q: 4. Find fyryzyaz, if f(r, y) = x² cos[100(e" + /1+ y²)®]

A: Given; f(x,y) = x2cos[100(ey+√(1+y2))y]

Q: Find constants c1 and c2 such that: F(x) = c1 sin(3x) + c2x cos(3x) is an antiderivative of f(x) =…

A:

Q: Qg:- Prove that fcz) = cx-y') + %3D are harmonic function f xy) ,but are not. hormonic conjugates.

A: This problem is related with complex analysis. Given that,                   fz = x2 - y2 + yx2+y2 i…

Q: Solve if the set of functions (1, x, sin x, e^x, cos x) is linearly independent or dependent…

A:

Q: 1. If f(x, y)=3x' sin y- y² cos x- 2yln x– xh y- 4xy , find- of ôf ô²ƒ ô²ƒ

A: Given: fx,y=3x3siny-y2cosx-2ylnx-xlny-4xy2

Q: Consider the function f(x) = cos x − 3x + 1. Since f (0)f() <0. f(x) has a root in [0]. If we use…

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Q: Find !V1-cos xdx 2 sin x = 1- COS X V2(-cos x/2)+ c 1/ /2(-cos x/2)+ c В. 2/2(-cos x/2)+ c С.…

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Q: Consider the following IVP: y" + y' = -cos x; y(0) = a, y'(0) = b Find the general solution. y(x) =…

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Q: Let f(x) = 2x? cos(4r). %3D f'(x) = - 8x sin(4x) + 4x cos(4x) COS f'(2) = %3D f"(x) =|| 0 f"(2) =| |

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Q: dy Find as a function of x when y = sin°(x) %3D O 1) 5cos (x) 2) 5sin (x)cos(x) 3) 5sin (x) 4) 5cos…

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Q: Differentiate the following functions (prob 8. 4x2 + 3y2 – 3x = 20 %3D 9. cos(x) + sin(3y) = 3

A: When we differenciate w.r.t "x" y become constant.

Q: Suppose that z is a function of z and y and that ze y cos z. Find and

A:

Q: If f(x,y,z)=In(x²y+sin² 12

A:

Q: Show that (Aetkx + Be-ikx)and (C cos kx + D sin kx) are equivalent ways of writing the same function…

A: eix  = cos(x) + i sin(x) e-ix = cos(x) - i sin(x)

Q: Q5: find 2 for the following functions: a) y = asin(2/x)+ csc(4x) + tan(x*) b) y = sin(e) +…

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Q: If f(x) = sin(x)e2x, then f"(x) = A) 3sin(x) e2x + 4cos(x) e²*. B) 3sin(x) e2x + 2cos(x) e²x. C)…

A: The given function is: f(x)=sin(x)e2x to find the second derivative f''(x). For that one has to find…

Q: Solve using the false rule method f(x) = /x² + 1 – tan x %3D starting at the interval [0.5,1]

A:

Q: dt, evaluate F(0) and F'(0). Given F(x) = Ju- 5. %3D J1+sin(2x) 1+ et-1

A: We have to find out

Q: Find dy if y= 5x² sin4x dr O None -20x? cos4x – 10xsin4x 20x² cos4x + 10xsin4x O 10x² cos4x +…

A: We apply u*v rule of derivatives d/dx (u*v) = v*du/dx + u *dv/dx

Q: A force of F(x)=x²-cos(3x) +2, x is in meters, acts on an object. What is the work required to move…

A: Given force f(x)=x2-cos(3x)+2

Q: Suppose u = u(x) is a function depending on x. Then, cos(u?x) equals 1. – sin (u²x); 2. – sin (u?x)…

A: Given: Let u = u(x) is a function depending on x.   To determine: ddxcosu2x   Formula used: The…

Q: Determine f,(x); f(x) = cos(2x³ +n²)

A:

Q: 3. Determine the exact value of f"(0) for f(x) = (cos5x + 5x²)*.

A: Given

Q: b) verify the functions sin(3x) and cos(3x) are linear dependent or Linear independent.

A: Hence linear independent

Q: 9. Evaluate y' of y = e-2*sin3x a. 3e-cos3x- 2y b. 3e-cos3x- 3y c. 3ecos3x - y d. 3e-cos3x +y e. Not…

A: Explanation of the answer is as follows

Q: Consider the function f(x) = cos x − 3x + 1. Since ƒ (0)ƒ (1) < 0. f(x) has a root in - [o,]. If we…

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Q: Show that U(,y) is Harmonic function and find its conjugate for U(x, y) = 2x – x³ + 3xy² -

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Q: The domain of the function f defined by is equal to: Select one: O True O False 7 cos(x)+y² In…

A: This question is based on logarithmic function.

Q: Compute Cos (x + k ) cos a dx by using substitution technique where k is a constant. [Hint: cos(A±…

A: The given integral is cos(x+k)/cosx.

Q: 4. Find f'(x) if f(x)= In (2x) + cos (6x)

A: Given- f(x)=ln(2x)+cos(6x) To find - f'(x) Here we will use the following formulas-…

Q: If A =x 2sinyi+z?cosyj -xy2k then -=x?cosyi - z?cosyj-2xyk 1O ду =x?cosyi-z2sinyj-y?k ду .II O…

A: We use partial derivatives to answer the given question.

Q: 3. If w-f(x.y) and x-r.cose, y-r.sin6 Prove that - A + fy ar

A: Given that w=f(x,y) and x=rcosθ,y=rsinθ Prove that ∂w∂r2+1r2∂w∂θ2=fx2+fy2

Q: Suppose f(x) =sin(3x- 2). Evaluate: A -3cos(3x- 2) +C B ® --cos( 3x – 2) +C © ;cos(3x – 2) + C D D…

A: Topic = Integration Correct option = B

Q: If it was f(x,y)=y cos(6xy) SO a² f Əy² 2² f Əy² a² f Əy² a² f Əy² = 36 x²y cos(6xy) + 12x sin(6xy)…

A: A detailed solution is given below.

Q: ,In sec²(sin2y)dy can be evaluated by writing it as sec2y ! / sec²( sin2y) - 2 cos2ydy S. | sec2(…

A: To simplify the given integral.

Q: Consider the function f(x) = cos x - 3x + 1. Since f (0)f () <0, f(x) has a root in [0]. If we use…

A:

Q: f f(x,y) = 8-2x3-6xy-3y2 and if x = (r-3)cos(s+1) and y = (r-1)/(r+s), using chain rule, find ∂f/∂r…

A:

Q: Consider the following IVP: y" + y' = -cos x; y(0) = a, y'(0) = b Find the general solution. @ y(x)…

A: We find the general solution of given DE  y"+y'=-cos(x)........(1)

Q: If u(x; y) = e sin x - x. Show that u(x, y) is harmonic and find its harmonic conjugate v(x, y) to…

A: Given that ux,y=e-ysinx-x The partial derivatives of u are,…

Q: Consider the following IVP: y" + y' = -cos x; y(0) = a, y'(0) = b Find the general solution. A y(x)…

A:

Q: If f(x) = f = Stanu √I+1² 0 1+e' In (secx)√1+tan²x (A) tanx 1+e sec ³x В) Ⓒ (D) tanx 1+tan²x 1+e…

A: Application of integration

Q: If f(x)= (A) B D plans √ 1+1² tanx I+e' f sec ³x tanx 1+tan²x Itefan 1+e -dt, then f'(x) equals…

A:

Rate of Change

The relation between two quantities which displays how much greater one quantity is than another is called ratio.

Slope

The change in the vertical distances is known as the rise and the change in the horizontal distances is known as the run. So, the rise divided by run is nothing but a slope value. It is calculated with simple algebraic equations as: