All tools › Calculus
Limit
From each side, with the table of approach that is the evidence
It runs entirely in this browser tab: what you type is never uploaded, and the arithmetic is exact — nothing here was ever a floating-point number.
Settings
- Variable
- Which letter to work with, when there is more than one
- At the point
- Where to work the value out, if anywhere
- From
- Choices: From both sides, From the left, From the right.
- Decimal places
- How far an approximate answer is taken A number from 2 to 12.
- Table of approach
- The evidence for the limit, which one number is not
How to use it
- Paste your text into the box above, or open a file.
- Adjust the settings beside it until the result is what you wanted.
- Copy the result, or save it as a file. The result updates as you type.
Questions
- Is what I type uploaded anywhere?
- No. The whole application is carried as WebAssembly and runs on your own device. There is no server to send anything to, and none of these tools makes a network request while it works.
- Why does it matter that there is no floating point?
- Because these tools show their working. In floating point an elimination produces rows with 0.0000000000000002 where a zero belongs, and every step after it is decided by a tolerance somebody picked. In fractions the zero is a zero: the rank is a count, a determinant of a matrix of thirds is a third, and a matrix times its inverse is exactly the identity.
- Can I use it in an exam or for homework?
- That is between you and whoever set the work. What these give you is the method as well as the answer, which is usually what is being marked: the rule at each step, the substitution written out, the intermediate matrices, the table of values.
- Why does a tool sometimes refuse instead of answering?
- Because the honest answer is sometimes that there is none. An integral with no elementary antiderivative, a matrix with no inverse, a bisection over an interval with no sign change, a logarithm of zero: each is a fact rather than a failure, and a plausible number in its place would be worse than the refusal.
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