If x --> 0+ (x tends to zero from the right), then its logarithm tends to minus infinity. On the other hand, x --> 0- (x tends to zero from the left) makes no sense, at least for real numbers, because the logarithm of negative numbers is undefined.
1 divided by 0 is infinity. So you can't really write it as a decimal. It is not technically possible to divide something by 0. Seriously, try entering it into a calculator. I know for a fact that on mine it has a special 'divide by zero' error. Yes, I was a bit hasty saying it was infinity. In fact mathematicians say a number divided by zero is "undefined". As you divide 1 by smaller and smaller numbers the result "tends to infinity" as the "limit".
Sine does not converge but oscillates. As a result sine does not tend to a limit as its argument tends to infinity. So sine(infinity) is not defined.
One way to find a vertical asymptote is to take the inverse of the given function and evaluate its limit as x tends to infinity.
It depends what the number is: f the number is not zero you get an error as it cannot be done. If the number is zero you get any number you want. This is used in calculus as the limit of a division where the dividend and divisor both tend towards zero: the limit is zero divided by zero, but as the numbers tend towards zero the division tends towards a value. For example, if a chord is drawn on a circle as one point moves towards the other, the slope of the cord (as calculated by the gradient between the two end points) tends towards the slope of the tangent at the point which is not moving - when the points coincide you have zero divided by zero and this is the slope of the tangent at the point!
If x --> 0+ (x tends to zero from the right), then its logarithm tends to minus infinity. On the other hand, x --> 0- (x tends to zero from the left) makes no sense, at least for real numbers, because the logarithm of negative numbers is undefined.
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In general, for a continuous function (one that doesn't make sudden jump - the type of functions you normally deal with), the limit of a function (as x tends to some value) is the same as the function of the limit (as x tends to the same value).e to the power x is continuous. However, you really can't know much about "limit of f(x) as x tends to infinity"; the situation may vary quite a lot, depending on the function. For example, such a limit might not exist in the general case. Two simple examples where this limit does not exist are x squared, and sine of x. If the limit exists, I would expect the two expressions, in the question, to be equal.
Since x is not a part of the expression, x can approach zero without any effect. So, the answer would be (tank-sink whole)/k, k<>0.
limit x tends to infinitive ((e^x)-1)/(x)
None, although "perfect square" tends to be used for whole numbers.
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The difference can probably be stated more explicitly in mathematical terms."x tends to 0" typically implies that x is an independent variable of an unstated function. You are evaluating the function as this variable tends to zero; or, limx→0 f(x)."limit of x tends to 0" instead implies that "x" is the function, and the value of it as you approach some unstated value tends to 0; or, lima→b x(a) = 0 where "b" is the value the function is approaching, whether real or ±infinity.
1 divided by 0 is infinity. So you can't really write it as a decimal. It is not technically possible to divide something by 0. Seriously, try entering it into a calculator. I know for a fact that on mine it has a special 'divide by zero' error. Yes, I was a bit hasty saying it was infinity. In fact mathematicians say a number divided by zero is "undefined". As you divide 1 by smaller and smaller numbers the result "tends to infinity" as the "limit".
They can. There is no age limit on this, it is judged on the quality. However, as a general rule, quality tends to come with age. :)
The limit is 2. (Take the deriviative of both the top and bottom [L'Hôpital's rule] and plug zero in.)
I believe the maximum would be two - one when the independent variable tends toward minus infinity, and one when it tends toward plus infinity. Unbounded functions can have lots of asymptotes; for example the periodic tangent function.