Use l'Hospital's rule: If a fraction becomes 0/0 at the limit (which this one does),
then the limit of the fraction is equal to the limit of
(derivative of the numerator) / (derivative of the denominator) .
In this case, that new fraction is sin(3x)/cos(3x) .
That's just tan(3x), which goes quietly and nicely to zero as x ---> 0 .
Can't say why l'Hospital's rule stuck with me all these years.
But when it works, like on this one, you can't beat it.
The answer will depend on any parentheses present in the expression. Until these are given explicitly, it is not possible to answer the question.
As X approaches infinity it approaches close as you like to 0. so, sin(-1/2)
Actually 0/0 is undefined because there is no logical way to define it. In ordinary mathematics, you cannot divide by zero.The limit of x/x as x approaches 0 exists and equals 1 so you might be tempted to define 0/0 to be 1.However, the limit of x2/x as x approaches 0 is 0, and the limit of x/x2 as x approaches 0 does not exist .r/0 where r is not 0 is also undefined. It is certainly misleading, if not incorrect to say that r/0 = infinity.If r > 0 then the limit of r/x as x approaches 0 from the right is plus infinity which means the expression increases without bounds. However, the limit as x approaches 0 from the left is minus infinity.
The "value" of the function at x = 2 is (x+2)/(x-2) so the answer is plus or minus infinity depending on whether x approaches 2 from >2 or <2, respectively.
12.600000000000001
The answer will depend on any parentheses present in the expression. Until these are given explicitly, it is not possible to answer the question.
As X approaches infinity it approaches close as you like to 0. so, sin(-1/2)
Actually 0/0 is undefined because there is no logical way to define it. In ordinary mathematics, you cannot divide by zero.The limit of x/x as x approaches 0 exists and equals 1 so you might be tempted to define 0/0 to be 1.However, the limit of x2/x as x approaches 0 is 0, and the limit of x/x2 as x approaches 0 does not exist .r/0 where r is not 0 is also undefined. It is certainly misleading, if not incorrect to say that r/0 = infinity.If r > 0 then the limit of r/x as x approaches 0 from the right is plus infinity which means the expression increases without bounds. However, the limit as x approaches 0 from the left is minus infinity.
The "value" of the function at x = 2 is (x+2)/(x-2) so the answer is plus or minus infinity depending on whether x approaches 2 from >2 or <2, respectively.
Plus
÷/÷ = +
4 divided by 9 minus 1 divided 12?
12.600000000000001
-3
(-9) / 3 = -3 . Minus nine divided by three is equal to minus three
6 divided by 11 minus 1 divided by 2 equals?
-3