BSc Mathematics SEM IV 2017 18 2017-18 MATHS I Question Paper - Mumbai University | munotes

Questions asked in this paper

1. Q3 De 1 IR? Using it prove that find directional derivative of f(x,y) a (0, 0) exist but fis not differentiable at (0, 0) function of n variable al line of the surface yz = log (x +z) at (0, 0, 1) 2 be a differentiable at then for any unit able at then f +g is also differentiable at P a > be a differentiable at Pe, then fis continous at
   • g.3 A) Attempt any one
2. Q1 State and prove Mean Value inequality for vec or fiel
3. Q9 Find the point on ellipse x? + = 4 where fix, y) = xy
   • B) Attempt any three
4. Q1 Define Jacobian matrix of vector valued fix, y) = cosy, y sinx) at (
5. Q2 Prove that derivative of vector valued
6. Q3 Using Taylor's theorem, Expand the
7. Q4 Define Linear approximation. linear ap
8. Q4 Attempt any three
9. Q1 Using derivative test the function f(x, y
10. Q2 Define Hessian matrix. Find Hessian matrix ai a
11. Q3 Let f: IR? be a function given by f(x, y) =(|x| that if f is continuous at (0, 0) by proving that 4 marks
12. Q4 Define Partial derivative of function. Find partial deri
    • y) = 4x? + 3xy +y?+8x+yat(0,0)
13. Q5 State and prove chain rule for derivative of s alar field

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