111) d
2)what u wanna prove by saying that
(a) lim x→a f(x) is integer
(b) lim x→a f(x) is non integer
U wanna say like a number is odd and still it is even[11]
1) If k sin2x + (1/k) cosec 2 x = 2, for all x belonging to (0, pie/2) then cos2x + 5 sinx cosx + 6 sin 2x is equals to
(a) (k2+5k+6) / k2
(b) (k2-5k+6) / k2
(c)6
(d) none of these
choose the correct alternative
2) If lim x→a f(x) = lim x→a [f(x)] (where[.] denotes the greatest integral function) and f(x) is non constant continous function, then show that
(a) lim x→a f(x) is integer
(b) lim x→a f(x) is non integer
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9 Answers
106ksin2x + 1ksin2x = 2
As k>0, we have x+1/x=2
i.e. ksin2x = 1
=> sin2x = 1/k
So u can obtain the result
11
1Ques2 was given in the book as
2) ) If lim x→a f(x) = lim x→a [f(x)] (where[.] denotes the greatest integral function) and f(x) is non constant continous function, then
(a) lim x→a f(x) is integer
(b) lim x→a f(x) is non integer
(c) f(x) has local maximum at x=a
(d) f(x) has local minima at x=a.
And the asn given was (a), (b)
66I wonder why these questions are supposed to be only for the three of us. And obviously you need to change your book.
62yeah.. there are a few really good guys here... Why have these questions to be for us alone :)
and the book has a typing error.. I wouldnt exactly say what anant sir has said.. but yeah you have to be careful when using the book.. This question for instance is a decent question :) (only the answer is incorrect)
1Ans of second ques is only (a) lim x→a is integer
@Nishant sir, yes there was some printing error.