= Evaluate and at the point (7, 7, «) using the implicit relation sin(z + y) + sin(y + z) + sin(z + 2) = 0.

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A: Given: f(x)=|cosx|

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A:

Q: 25) Use Dr. Dai's Differential Table to find [tan - 1(x) ]' =, 25) A) 1/ (1+ x2) B) – tan-2(x) sec2x…

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A: *Use chain rule

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Q: IT ) Verify that ,0) is a critical point of f(x, y) = y² - 2y cos x. Then use the second derivative…

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Q: With mean theorm, show that | cos x - cos y| < ]x – yl for all of x and y at R www.wwwnn

A: Mean Value theorem

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A: As per guidelines we can solve only one question at a time. So the first question can be solved as…

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Q: + Bsin z Differentiate @ wi th xespect to x - - S"d (use dy A sinz + B cose

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A: The basic relations we need to know to solve this problem are, sinh(x) = ex- e-x2cosh(x) = ex+ e-x2

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A: We have to prove

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Q: 3.44 3. Test for homogeneity f (x, y) tanx-sec²x - cosy

A: Question : Test for the homogeneity f(x, y) = tanx - sec²x - cosy

Q: 4. Interval 0<x<n, function, f(x) = sin 2x. %3D

A: We have to find the Fourier series of the function fx=sin2x ,x∈0,π

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Q: hich the extrema occur. g(x)=x^2+cos⁡(x^2 ) on [-√π,√π]

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Q: 4 Test for homogeneity fx,y)- tanx- see'x - Osy

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Q: of of +y y Let f(x, y) = x$y² tan Then x equals X

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Q: 5. Verify whether the function f(z) Cauchy-Riemann equations or not. sinh 4x cos 4y + i cosh 4x sin…

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Q: Sketch the graph of two functions g(x) = cos x and h(x) = on the same plane. Choose [a, b] that…

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Q: by using mean value theorem prove |sin(x) – sin(y)I < ]x – y|

A: To prove sinx-siny≤x-y Let f(t)=sint ∀t∈(x,y) Then we have the mean value theorem f'(c)=f(x)-f(y)x-y…

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Q: Suppose that f(x, y) = x°y. The directional derivative of f(x, y) in the directional (– 2, – 1) and…

A: Explained below

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A: First find gradient at point and take dot product with unit vector

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Q: (2x) Sinx 2. Prove that (1) Jy₂ (x)=√√(x) =_ (11) J-y₂(x) = √(3/1²) Cosx

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Q: If y=tanx , prove that y```=2(y^2+1)(3y^2+1)

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Q: Of of Let f(x, y) = x°y² tan y Then x +y. equals

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Q: Find all transition points for the interval [0, 2]. 3 y = 3x + sin(3x) %3D

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Q: B) Prove that: cosh (x + y) = coshx coshy + sinhx sinhy %3D

A: We know that cosh(θ) = eθ+e-θ2sinh(θ) = eθ-e-θ2

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A: Introduction :

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A: NOTE: Refresh your page if you can't see any equations. . ..............(1) substitute  take…

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Q: the Prove function is analytic at z = 0. By calculating all the directional derivatives of the that…

A: The given function is ; f(z) = z¯2z,if z&gt;00,if z=0 We have to show that the function f(z) is not…