## Quick Reference

The statement that *f*(*x*) tends to *l* as *x* tends to *a* from the left can be written: *f*(*x*)→ *l* as *x* → *a*−. Another way of writing this is

The formal definition says that this is so if, given *ε*>0, there is a number *δ*>0 such that, for all *x* strictly between *a*−*δ* and *a*, *f*(*x*) lies between *l*−*ε* and *l*+*ε*. In place of *x* → *a*−, some authors use *x* ↗ *a*. In the same way, the statement that *f*(*x*) tends to *l* as *x* tends to *a* from the right can be written: *f*(*x*) → *l* as *x* → *a*+. Another way of writing this isThe formal definition says that this is so if, given *ε*>0, there is a number *δ*>0 such that, for all *x* strictly between *a* and *a*+*δ*, *f*(*x*) lies between *l*−*ε* and *l*+*ε*. In place of *x* → *a*+, some authors use *x* ↘ *a*. For example, if *f*(*x*)=*x*−[*x*], then

*Subjects:*
Mathematics.

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