M0IITU13 - Functions, limits &amp; continuity qns

# M0IITU13 - Functions, limits &amp; continuity qns -...

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1 QUEST TUTORIALS Head Office : E-16/289, Sector-8, Rohini, New Delhi, Ph. 65395439 1. If f(x) = cos (log x), then f(x) f(y) - 1 2 ( ) [ ] f x y f xy + ( ) = (A) - 1 (B) 1 2 (C) - 2 (D) None of these 2. If f(x) = x x x x sin , , 1 0 0 0 = , then Limit x 0 f(x) = (A) 1 (B) 0 (C) - 1 (D) None of these 3. The function, f(x) = log ( ) log ( ) 1 1 + - - a x bx x is not defined at x = 0 . The value which should be assigned to f at x = 0, so that it is continuous at x = 0, is : (A) a - b (B) 1 + b (C) log a + log b (D) None of these 4. Let f(x) = x x x x if x k if x 3 2 2 16 20 2 2 2 + - + - = ( ) , , If f(x) be continuous for all x, then k is equal to : (A) 7 (B) - 7 (C) ± 7 (D) None of these 5. Limit x 1 (1 - x) tan π x 2 = (A) π 2 (B) π + 2 (C) 2 π (D) None of these 6. In order that the function, f(x) = (x + 1) 1/x is continuous at x = 0, f(0) must be defined as : (A) f(0) = 0 (B) f(0) = e (C) f(0) = 1/e (D) f(0) = 1 7. Domain of the function, sin l n 4 1 2 - - x x is : (A) [- 2, 1] (B) (- 2, 1) (C) [- 2, 1) (D) (- 2, 1] 8. If f(9) = 9, f (9) = 4, then Limit x 9 f x x ( ) - - 9 3 = (A) 2 (B) 4 (C) - 2 (D) - 4 9. Limit h 0 x h x h + - = (A) 1 2 x (B) 1 x (C) 2 x (D) x 10. Limit x 0 2 1 1 1 1 2 x x - + - ( ) / = (A) log 2 (B) log 4 (C) log 2 (D) None of these 11. If f(x) = x x x for x for x 2 2 4 3 1 1 2 1 - + - = , , then : (A) Limit x → + 1 0 f(x) = 2 (B) Limit x → - 1 f(x) = 3 (C) f(x) is discontinuous at x = 1 Function, Limits & Continuity

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QUEST TUTORIALS Head Office : E-16/289, Sector-8, Rohini, New Delhi, Ph. 65395439 (D) None of these 12. If f(x) = sin cos x x x when x when x + = 0 2 0 then : (A) Limit x → + 0 f(x) 0 (B) Limit x → - 0 f(x) = 0 (C) f(x) is continuous at x = 0 (D) None of these 13. Limit x π 4 sin cos α α α π - - 4 = (A) 2 (B) 1 2 (C) 1 (D) None of these 14. Limit x π 2 tan x log sin x = (A) 0 (B) 1 (C) - 1 (D) None of these 15. Limit x 0 tan sin 2 3 x x x x - - = (A) 0 (B) 1 (C) 1 2 (D) 1 3 16. Limit x 0 cos cos a x bx x - 2 = (A) a b 2 2 2 - (B) b a 2 2 2 - (C) a 2 - b 2 (D) b 2 - a 2 17. If f(x) = x x x x x - < = > 1 1 4 0 0 0 2 , , , , then : (A) Limit x → + 0 f(x) = 1 (B) Limit x → - 0 f(x) = 1 (C) f(x) is discontinuous at x = 0 (D) None of these 18. The value of Limit x → ∞ x bx x ax 2 2 4 5 + + + + is (A) b a (B) 1 (C) 0 (D) 4 5 19. Limit x 0 - x b a x x = (A) log b a (B) log a b (C) a b (D) log a b 20. If f(x) = [ ] [ ] sin , [ ] , [ ] x x when x when x 0 0 0 = where [x] is greatest integer function, then Limit x 0 f(x) =
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## This note was uploaded on 10/05/2011 for the course MATH 1201 taught by Professor Friesner during the Spring '11 term at St. Mary NE.

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M0IITU13 - Functions, limits &amp; continuity qns -...

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