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Solve the Laplace equation ( \frac\partial^2 u\partial x^2 + \frac\partial^2 u\partial y^2 = 0 ) for a rectangular plate with boundary conditions: ( u(0,y)=0, u(a,y)=0, u(x,0)=0, u(x,b) = \sin\left(\frac\pi xa\right) ). (7 marks) Unit – D: Laplace Transforms Q7 (a) Find the Laplace transform of: (i) ( t^2 e^-3t \sin 2t ) (ii) ( \frac1 - \cos att ) (7 marks)

Find the radius of curvature for the curve ( y = a \log \sec\left(\fracxa\right) ) at any point. (7 marks) higher engineering mathematics b s grewal

B.Tech / B.E. – Semester I / II Examination Subject: Higher Engineering Mathematics (MA-101) Code: [As per your scheme] Solve the Laplace equation ( \frac\partial^2 u\partial x^2

Evaluate by Simpson’s 3/8 rule: [ \int_0^6 \fracdx1 + x^2 ] taking ( h = 1 ). (7 marks) – Semester I / II Examination Subject: Higher

Find the inverse Laplace transform of: [ \fracs^2 + 2s + 3(s^2 + 2s + 2)(s^2 + 2s + 5) ] (7 marks)

Find the volume of the sphere ( x^2 + y^2 + z^2 = a^2 ) using triple integration in spherical coordinates. (7 marks)