Question

What is `lim_(t-> 0) (1/t -1/t^2-t)`?

Answer 1

`lim_{x to 0}(1/t-1/t^2-t)=lim_{x to 0}(t-1-t^3)/t^2=lim_{x to 0}-1/t^2=-infty`

Explanation:

In cases one has to deal with sums of powers and fraction of powers which lead to the indeterminate form `infty - infty`, it's often a good idea to reduce the expression to a big, unique fraction.