can u tell me ? Lim [Sin x] when x limited to the 90 degree( from right and left limited ) . what is answer ?

Question

[ ] this sign for bracket not ( ) .

my mean about bracket is : for sample : [ 1.5] = 1 or [3.8] = 3 ....
now i want know why that answer is : zero both left and right .

Answer 1

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The limit of the ceiling function/greatest integer function of sine of x when x approaches 90 degrees is 0.

This is because whether x approaches 90 degrees from the left or the right, the value of sine of x at that point has to be slightly lesser than 1 (sine at 0 degrees is 0 and increases until it attains its maximum value of 1 which is only at the 1 particular point - 90 degrees and beyond which sine starts decreasing to reach 0 at 180 degrees). And the ceiling function of this number slightly lesser than 1 will be 0.

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Answer 2

Since sin x is a continuous function, the limit of sin x at any point should be the same as its defined value at the point.

Lim [Sin x] when x limited to the 90 degree = sin 90 = 1

Answer 3

Lim (x→90 +) sin x = 1

Lim (x→90 -) sin x = 1

They are the same because the function f(x) = sin x is both continuous and defined at x = 90.

Answer 4

Do you mean what is limit of sine(x) as x approaches 90 degrees?

If so, the answer is one.

Answer 5

-1<=sinx<=1 since it is a continuos function.
when lim(x-->90-), sinx=1
and lim(x-->90+), sinx=1
therefore lim(x-->90), sinx=1

Answer 6

Is there any particular reason that [ ] brackets are important, rather than ( ) brackets?