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###### Jinesh Jain posted an Question
February 08, 2022 • 16:16 pm 30 points
• IIT JAM
• Mathematics (MA)

# Ueonstirute power series and function of several variables 17. if f:r >r is defined by 21. if (x. y) = (0,0), suppose (c)is a sequence of real numbers s(x. y)=r

ueOnstirute Power Series and Function of several variables 17. If f:R >R is defined by 21. if (x. y) = (0,0), Suppose (C)is a sequence of real numbers S(x. y)=r+y (&, y) = (0, 0). such that limlc.exists and is non-zero. If 0 if (x, y) = (0, 0), n the radius of convergence of the power series then 2,xis equal to r, then the radius of (a.) S.(0, 0) = 0 and f, (0,0) = 0 n=0 convergence of the power series nc, is (b.) f.(0,0) = 1 and f, (0, 0) = 0 (c.) f.(0,0) =0 and f, (0,0) =1 (a.) less than r (b.) greater than r (d.) S.(0,0) and ,(0, 0) =1 (c.) equal to r If the power series a,x converges for (d.) equal to 0 18. 22. Let f:R>R be defined by n=0 x= 3,then the seriesa,x f(. y)=+y ( y) = (0, 0), 0 if (x. y) = (0,0) (a.) Converges absolutely for x= -2 (b.) Converges but not absolutely for x=-1 Which of the following statements holds regarding the continuity and the existence of partial derivatives of f at (0,0)? (c.) Converges but not absolutely for x = 1 (d.) Diverges for x = -2 19. The set of all x at which the power series (a.) Both partial derivatives of f exists at n (0,0) and f is continuous at (0, 0) 2 r-2) converges is a (2n+1 (b.) Both partial derivatives of f exists at (a.) -1, 1) (0,0) and f is NOT continuous at (b.) -1, 1 (0,0) (c.) [1. 3) (c.) One partial derivatives of f does NOT exist at (0,0) and f is continuous at (d.) [1, 3 (0,0) (d.) One partial derivati ves off does NOT exists at (0,0) and f is NOT continuous if n is prime 20. Let a, = A f nis not a prime at (0,0) of Then the radius of convergence of the power Then +y ar 0dy 23. Let f(x. y) =ry' tan " series a,r is n equals (a.)4 (a.) 2f (b.) 3 (b.) 3f (c.) (c.) Sf (d.) IT Nrw Pelhi-110016, Ph: (011)-26537527, Cell: 9999183434 & 9899161734, 8588844789 Cadeomy.com 190 question no. 17, 18, 19, 20, 21, 22

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