Higher Engineering Mathematics B S Grewal !!top!! Direct

B.Tech / B.E. – Semester I / II Examination Subject: Higher Engineering Mathematics (MA-101) Code: [As per your scheme]

If ( u = \log(x^3 + y^3 + z^3 - 3xyz) ), prove that: [ \left(\frac\partial\partial x + \frac\partial\partial y + \frac\partial\partial z\right)^2 u = -\frac9(x+y+z)^2 ] (7 marks) higher engineering mathematics b s grewal

Trace the curve ( r = a(1 + \cos\theta) ) (Cardioid) and find the area enclosed. (7 marks) Unit – B: Multiple Integrals & Vector Calculus Q3 (a) Evaluate: [ \int_0^1 \int_0^\sqrt1-x^2 \int_0^\sqrt1-x^2-y^2 \fracdz , dy , dx\sqrt1-x^2-y^2-z^2 ] (7 marks) higher engineering mathematics b s grewal

Evaluate by Simpson’s 3/8 rule: [ \int_0^6 \fracdx1 + x^2 ] taking ( h = 1 ). (7 marks) higher engineering mathematics b s grewal