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Q: The derivative of f(x,y) at P. (1, 2) in the direction of its is 2√2 and in the direction of the #…

A: The given problem is to find the directional derivative of the function f at point (1,2) in the…

Q: r5TT T Show that fi (x) = e* , f2(x) = sin x are 4 '4

A: Use standard innerproduct of L2 space

Q: √²³₁(−12xy² + 8x³y + 3)dxdy

A: LetWe have to evaluate the above integral.

Q: EXAMPLE 3 Derivative rules Compute the following derivatives, where u(t) = ti + ťj –- tk and v(t) =…

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Q: Calculus I May I please have the solutions for the following questions? Thank you,

A: Given equations :(a) x3−xy2+y3=1Differentiating both sides w.r.t. x…

Q: Question 2 By using appropriate properties, find F (s) for the function f(t)=(t+3e" )sin(41)

A: The solution is given as

Q: Find the maximum rate of change of f at the given point and the direction in which it occurs. f(x,…

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Q: Q4) Find y" + 2y' + 5y where y cos(1/secx)

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Q: The temperature T in a metal ball is inversely proportional to the distance from the center of the…

A: The given problem is to find the rate of change of temperature at point (2,4,4) in the direction…

Q: 7 The Laplace inverse of L- is s2 + 72 O sin(7t) O cos(7t) O cos h(7t)

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Q: Use the Convolution Theorem and this example to evaluate the given Laplace transform. Do not…

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Q: 1 (ii) Lª. 1+/s]

A: The solution are next step

Q: 2. Find the Laplace Transforms of (te' sin(at))" when a = 1

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Q: Calculus I May I please have the solutions for the following questions? Thank you,

A: Step 1: Step 2: Step 3: Step 4:

Q: Shift Operator, Forward & Backward Difference Operator

A: We have to solve the given expression  ∆2E∇3e16xsin37x

Q: Find the derivative. r=3-0³ cos 0 dr OA. de OB. O C. O D. dr de dr de dr de == 30² sin 0 =30² sin 0…

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Q: 10. Prove that 7/2 TC sin 0 cos (cos a cosec 0) de 2-a (1-cos a). COS

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Q: Derivative rules Compute the following derivative.

A: Given: y=t3i+6j-2tk×3ti-12t2j-6t-2k. we have to find dydt for that first we find cross product  we…

Q: Show that L{cos at} = S s² + a² Hence find L{sin 8t sin 6t}.

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Q: The temperature T in a metal ball is inversely proportional to the distance from the center of the…

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Q: art8e ch03s03: Pro Problem Problem List Next Problem f f(x) = 3x sin z cos r, find f'(x).…

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Q: Use Theorem 13.9 to find the directional derivative of the function at P in the direction of PQ.…

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Q: Derivative rules Compute the following derivative.

A: To compute the derivative: ddt3t2i+tj-2t-1k.(costi+sin2tj-3tk)

Q: Calculus I May I please have the solutions for the following questions? Find the derivative of the…

A: In solving the following derivative, we only need to keep in mind the following chain rule:…

Q: y" + ay '- 3y sin 2x y o) =y'0) =12

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Q: Use the limit definition of a derivative to derive the function f(x) = √3x +1.

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Q: Q1: Use the table below to answer the following questions. I f(x) f'(x) g(r) g'(r) 1 -1 2 3 -2 1 -1…

A: The given function and derivative function values,xf(x)f'(x)g(x)g'(x)-21-124-13-2110-12-2-3The…

Q: En=1 sin(an n! U-

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Q: ze Find the Resi due of at its pole. (z-1)' z e (or) Find the poles and resi dues at each pole:…

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Q: Determine the directional derivative for f(x,y, z) = sin(yz) + In (x) at (1,1, 7) in the direction…

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Q: iii) sin(xy)=x³ + x²y. Ex 2. Find the derivative dy for the following then evaluate the derivative…

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Q: Calculus I May I please have the solutions for the following questions? Thank you,

A: Step 1:​ (a) f(t)=etsin(2t)f′(t)=dtd​etsin(2t)dxd​eax=aeaxChain…

Q: Solve by fourier finite cosine Date. Page. 4 ut * Solve By use [ Fourier Finite cosin:] uxx. 04X22…

A: Using finite Fourier cosine transform:

Q: sin5(θ) cos(θ) dθ     ,    u = sin(θ) find integral by making the given substitution

A: Substitute u=sinθ,du=cosθdθ.