3 Use the definition 平grien FuncTionsEat'co,): for ー X+y X-ツ ix=ツ ) fory) =) singty4) ーty2 (x) # CO,0)

Q: 10. Show that 2" + 42' + 8z = 0 if z = e-2=(sin 2x + cos 2x).

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Q: Evaluate the following limits

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Q: Then, the only positive equilibrium point of Eq.(1.1) is given by (2.7) (1 – A) (E Bi) Li=1 provided…

A: Given linearized equation of Eq(1.1) about y~ takes the form ;…

Q: e Divergence Theorem to evalu (4x + 10y + z²) dS Js

A:

Q: 16. f(x) = x' + x + 4 on (-1,2). 17. f(x) = x -x² – 30x + 3 on (0, 6). 18. f(x) = 3 sinx on [T/4,…

A:

Q: 3) Prove that c) cosh2x = 1 + 2 sinh? x

A: In the question we have to prove the given function.

Q: Find fy if f(x, y) = sin 5x cos 5y O fy = 5sin 5x sin 5y fx = cos 5x cos 5y O fx = 5cos 5y cos 5x fx…

A:

Q: 2. Let f(x, y, z) = In(x² + 2) + y²e#* - cos(2yz). Find fzyz-

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Q: Prove 8xyz < (x + y)(y + z)(x + z) for every x, y, z E [0, +∞[.

A: We have to prove given identity: Concept:

Q: 4. Find az/ax if z is a two variables function in x and y is defined implicitly by x5 + y² cos(x²₂³)…

A:

Q: п-(х-4)" 22и. (2n — 1) Ax) =En=0 n:

A: Solution of given problem as follow

Q: If xty= 2e Cos Øand x-y=2ies.m Ø show that Su

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Q: 2- Find the third derivative for əx3 for f(x,y) = sin) )+2 sin) sin)+3cos°) 8y3sinz s()+2sin()…

A:

Q: Let f(x) = -cos(x). Compute ộ = coto + C1T1 where to = 1 and 1i = x. %3D Compute the discrete…

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Q: 23. Given that f(0) = v2 cos (e-), the minimum value of o1+ v2 C. %3D COS D.-1 A. V2-1. B.2N2

A: Since you have posted multiple question in this question so I have solved first question as per our…

Q: If f(x,y,z)=In(x²y+sin² 12

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Q: 1. Use a Chain rule to find aw and ar aw , if w = x², x = sin(r²s) əs %3D

A: Given w = x2x = sin(r2s)

Q: If f(x) = Α) B C D tanx sec ³x 1 + e tanx 1+tan²x 1+ e tanx sec²x 1+1² 1+e' -dt, then f'(x) equals…

A: We have to find derivative of given integral.

Q: Suppose that z = xy² and x and y are differentiable func- tions of t with x =2,y = when t = -1. Then…

A:

Q: 4. A force of F(x) = x - cos(3x) + 2,x is in meters, acts on an object. Identify the work required…

A:

Q: 5. Show that cos x = x has a solution in the interval [0, 1]. Hint chow that f (x) = x cos x has a…

A: Given, Cosx =x

Q: 3. On (-∞, ∞), three functions y₁ (x) = cos 2x, y₂(x) = sin² x, y³(x) = cos² x are linearly…

A: Note: As per the guidelines we are supposed to only one answer because this is not a subparts…

Q: Which of the following is true? @ Jcos(3x)cos(4x)dx= [ cos(x) + cos(7x) 2 BAll of the above ©…

A:

Q: Are these equation separable 1.s2+ds/dt = (s+1)/st 2.dr= b(cosx dr+ rsinxdx) 3.y'=ye(x+y)/(x2+2)

A: The objective of the problem is to determine whether the given equations are separable. A…

Q: 5 of 9 > Let f(x, y, z) = 5x³ · y³ + z². Find the maximum value M for the directional derivative at…

A:

Q: (b) Show that the roots of y'(x) = 0 are x = 0, x = L, and x = L/2, so it follows (why?) that the…

A:

Q: question 31

A: Consider the given function.

Q: 7,2 Find the critical noint(s) of al r) and use the Second Derivative Test to classify the

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Q: Compute the derivatives of the given functions. f(2) = In (7z²). 7a?). f'(x): / (z) = help…

A:

Q: + 9y = 9 sin 3x (Let y p = Ax sin 3x + Bx cos 3x.) y = C1 sin 3x + C 2 cos 3x - x sin 3x + cos 3x y…

A:

Q: Compute the derivative of g(x) = | 1 dt. 2 1+t5 2" 1+æ15 1+25z 2" In 2 1+æ15 1+25z 2" 1+a15 1+25z 2"…

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Q: If  f(x,y,z)=ln(x2y+sin2(x+y))+227x228y2z229,  then    ∂4f ∂x2∂y∂z at (1,1,1)  is equal to

A: See the attachment.

Q: 5 The function f (x, y) =| x² cos² is homogenous in x and y of degree,

A:

Q: Evaluate: f(cos 5x - 2 sin 3x) dx O sin 5x - cos 3x + C Osin 5x - cos 3x + C O sin 5x+cos 3x + C…

A:

Q: Suppose that w = x² + y² – z² | And x = psin(4)cos(0), y = psin(4)sin(0), z = pcos(4) Use…

A: Simplify w by substituting values of x , y and z and then solve the partial derivative.

Q: Prove that v = In [(x-2)^2 + (y - N)^2] is harmonic in every region does not include .the point ( 2,…

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Q: Find az/əx and az/əy by implicit differentiation, In(1 +z) + xy² +z = 1 ye – 5 sin 3z = 3z %3D

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Q: Show that y1(t) = cos(3t) and y2(t) = sin(3t) are linearly independent for all t

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Q: 2. A. If : = sin(3x+2y) , verify that 2 -3 = -6z ax2 B. If f = x³y3 + 2xcosy + y?lnx then show that…

A: x=sin (3x+2y)

Q: Find az/ax if - z = x² sin(xy³) O x³y4 cos (yx³) + 4y³ sin(x³) O x³y³ cos (xy³) + 4x³ sin(xy³) x4y³…

A: Find the derivative

Q: In(8z) Siven f(z) the derivative f'(x) is 8. %3D O 8 8x o 1 O 78z 1 8x 1/8

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Q: 4) Differentiate each of the following: a) y = - cos²x c) f(0) = sin(20 — π) e) y = (52)²x g) y =…

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Q: 7.2 (A) 1. S sin x dx cos x + C because(-cos x +C) = %3D dx 2. S cos x dx = because sin x 3. S tan x…

A: We need to solve the given integral. This can be done as follows:

Q: Compute the derivative of y = In ( VI-2 conh z - (z² + 2) -(2- 1)

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Q: If f (x) = A) B (C) D tanx √1+1² 1+e' 0 1+tan²x tanx 1+e sec ³x -dt, then f'(x) equals tanx 1 + e In…

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Q: Show that the function f(z)=sin x cosh y+i cosx sinh y is continious as well as analytic every…

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Q: Exercise 3.1. Find the derivative of the following functions: y = tan 2x 2. g(x) = xsin x – 5 cos x…

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Q: Show that the functions In x , In(x2) linearly dependent (0, co) are on

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Q: H.co/ prove That;. dz 1-2 Cosh2=

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Numerical Integration

In a mathematical investigation, numerical integration comprises a wide group of calculations for computing the mathematical estimation of definite integral, and likewise, the term is moreover in some cases used to depict the numerical solution of differential equations. The most important aspect of this theory is error analysis.