1. Find the Laplace transforms for the given f(t). (h) f(t) = 3 sinh At (i) f(t) = e-2t cos 3t (j) f(t) = 4 + cosh 2t

Q: Find a harmonic conjugate of the function u(x, y) = arctan(x/y)− 6

A: Solution :-

Q: 1. Find the derivative of the following: 1² + 2r + 1 a) f(1) = r3 - 5x + 3 b) G(2) - VP+1 dt e) y…

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Q: . Determine the derivative of the following complex functions: f(z) = (z³ + 3z²)³at z = 2i b. Item…

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Q: Find fy ) for (x,y) Cos (x) sincy) exy

A: Given query is to find the partial derivative of the expression with respect to y.

Q: 2. Find the derivative (dy/dx) of the following functions: n) y = 1- cos 3x sin 2x + sin 8x tan 4x

A: 2) n) It is required to find the derivative of the function y=1-cos3xsin2x+sin8xtan4x.

Q: df Apply the first order backward difference representation of dx [f(x) = f(x − h)]/h vf = 2ππ L to…

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Q: d Find the derivative e" + sin ax] dx e" – a cos (ax) e" + a sin (ax) e" + a cos (ax) e" + sin (ax)

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Q: Consider the curve defined by r(t) = (cos(t) + t sin(t))+ (sin(t)- t cos(t))] for t > 0. (a) Compute…

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Q: Find f. f""(t)  =Cos t

A: To Determine: find f Given: we have f''''(t)=cost Explanation: we have…

Q: 4. Use implicit differentiation on these. a) Find an expression for dy/dx at any point on the curve…

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Q: Calculate when t = dr given that = (t – sin t) y = (1– cos t)

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Q: Find and sketch the odd and even components of the following functions r(t) = sin(wot)u(t) y(t) =…

A: We know that if a function is represented by f(t) Then even component of f(t) is  fe(t)=f(t)+f(-t)2…