IIT JAM Follow
December 1, 2020 2:46 pm 30 pts
19. Given that: M, = sup E xel |1+ x 2 where I is any closed interval. Then the sequence {fh}, where Sn)=- 2 XEI 1+ nx (A) converges pointwise to 0 B) converges pointwise to 1 (C) diverges (D) converges uniformly to 0 20. Iff(x, y) has an extreme value at (a, b), then (A) Sa,b) = 1 (B) Sa,b) = 2 (C) fa,b) +0 (D) (a, b) = 0 21. The remainder term in the Taylor's expansion of f(a+h, b +k) about the pa (a, b) is . (A) f(a + 0h, b +0k), 0<0<1 (B) -|f(a +0h, b +0k), 0<0<1 (C) f(a +0h,b +0k), 0<0<1 (D) None of these 22. Given that : 00 7 n=0 Then e . (B) n=0 n! (A) n n=0 (D) None of these (C) n=0