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B1A215S (2015 Admission) Total No. of pages: 3

PART 8

(Answer any 2 questions each question carries 7 marks)
a x n
Find the radius of curvature and interval of curvature of >, ‏لتب‎
‎n=! 2n+3
7 x ஜூ. x?
est the convergence of ಣಾ 3 + 34 +

Determine the Taylor’s series expansion of f(x) = sinx at x = 7/4.
(Answer any 2 questions each question carries 7 marks)

Find the nature of domain of the following function

f(xy) =x? -y?

2. f(x,y) = In(x? - 3)
3
⋅ xy
Show that the function /(x,y) = ‏كي‎ approaches zero as (x,y) -> (0,0)
‏مير‎ +}

along the line y = mx.

Find the trace of the surface x? + )2 - 22 = 011 the plane x = 2 and y = 1.
x? + y? _2₹-0
(Answer any 2 questions each question carries 7 marks)
Find the local linear approximation of f(x,y) = VQ? +7) at (3,4) and compare
the error in approximation by L(3.04,3.98) with the distance between the
points.
Find the relative extrema of f(x, y) =3x? - ‏بور2‎ y? - ‏بره‎

If z=e” ,x=2u+y, y=4 Find ட and ~
۷ Ou ov

(Answer any 2 questions each question carries 7 marks)
If r(t)=eli te ‏عا نر‎
1) Find the scalar tangential and normal component of acceleration at t = 0
2) Find the vector tangential and normal component of acceleration at t = 0.
Find the equation of the tangent plane and parametric equations of the normal

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