1 answer. It is not an indefinite form, for what is happening is clear. If f(x) approaches 0 from above, then the limit of p(x)f(x) is infinity. … If f(x) keeps changing sign as it approaches zero, then the limit of the quotient does not exist.
Why is infinity to the power of zero indeterminate?
There is no universal value for ∞0. It’s indefinite and the value depends on how you get ∞ and 0. … As for your actual question, ∑∞i = 1k1/k is infinite since you add a non-zero constant (k1/k) to itself infinitely many times.
Is infinity divided by 0 undetermined?
Indefinite form: 0 / 0 and infinity divided by infinity is indefinite. 29
What is infinity at 0?
In this case, infinity to the power of zero is equal to 1 because every real number to the power of zero is equal to 1. But if you’re calculating limits, infinity to the power of zero is indeterminate. For example: … There x is considered infinity while 1/x is considered zero.
Can you zero infinity?
Zero multiplied by infinity equals zero. … You might think it’s indefinite, because infinite times everything is infinite, but zero times everything equals zero. But we need to take a closer look. If you’re asking for infinity multiplied by zero, you’re literally adding zero infinite times.
Why is 1 to the power of infinity infinity?
That is, as x approaches infinity, the function gets closer and closer to the asymptote. Since the asymptote is a straight line that a curve approaches infinitely but never reaches, the function can never attain a real value at x= infinity. We therefore say that it is undefined.
What is the value of 1 to the power of infinity?
In general, it can be shown that unity to the infinity is the same for all x. That’s why we raise 1 to infinity to the power of infinity, just like division by 0, because it has many values and not just one. 8th
Is 1 divided by infinity?
Infinity is a concept, not a number, so the expression 1/infinity is actually indefinite. In mathematics, a limit of a function occurs when x increases as it approaches infinity and 1/x decreases as it approaches zero.
Can zero be divided by 1?
Answer: Zero divided by 1 is 0.
Is 0 times 0 defined?
0 / 0 is undefined. If replacing a value in an expression results in 0 / 0, there is a chance that the expression actually has a finite value, but it is not defined by this method. We use bounds (calculus) to determine this finite value. But we can’t just substitute and get an answer.
Is infinity a real word?
Infinity means many different things depending on when it is used. The word is of Latin origin and means endless. …Infinity is not usually a real number, but is sometimes used as such. Infinity often indicates how much of something there is rather than how big something is.
What is Ln infinity?
The limit of the natural logarithm of x as x approaches infinity is infinity: lim ln (x) = ∞ x→∞