MathGeek19
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- Apr 28, 2016
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- 6
\(\displaystyle \displaystyle \mbox{If }\, L\, =\, \lim_{x\, \rightarrow\, 0}\, \left[\dfrac{\sin(x)}{x}\right],\, M\, =\, \lim_{x\, \rightarrow\, 0}\, \left[\dfrac{x^2}{\sin(x)}\right],\, N\, =\, \left[\lim_{x\, \rightarrow\, 0}\,\dfrac{\sin^2(x)}{x}\right],\, \mbox{ and }\, O\, =\, \left[\lim_{x\, \rightarrow\, 0}\,\dfrac{x^2}{\sin(x)}\right]\)
\(\displaystyle \mbox{(where [.] denotes the Greatest Integer Function, or GIF), then L+M+N+O =?
. . .(1) 0 . . .(2) 1 . . .(3) 2 . . .(4) 3 or 4
I understand that N=O=0. What is confusing me is L and M.
Here, if I put the limits first in each of L,M,N and O then I might get the correct answer but how do I determine whether to use the limit first or The GIF first?(As far as I remember the limit can be taken outside as well inside the GIF)
GIF = Greatest Integer Function.
The correct answer is option (1).\)
\(\displaystyle \mbox{(where [.] denotes the Greatest Integer Function, or GIF), then L+M+N+O =?
. . .(1) 0 . . .(2) 1 . . .(3) 2 . . .(4) 3 or 4
I understand that N=O=0. What is confusing me is L and M.
Here, if I put the limits first in each of L,M,N and O then I might get the correct answer but how do I determine whether to use the limit first or The GIF first?(As far as I remember the limit can be taken outside as well inside the GIF)
GIF = Greatest Integer Function.
The correct answer is option (1).\)
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