The right-hand and left-hand limits are equal for most input values for most functions. This is commonly referred as limit of a function.

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Given that function `f(x)` evaluates to indeterminate value at `x=a`. To evaluate the expected value of `f(x)|_(x=a)`, we examine ;

• Left-hand-limit `lim_(x->a-) f(x)`

• Right-hand-limit `lim_(x->a+) f(x)`

If these two limits are equal then the result is referred as "*limit of the function at the input value*" `lim_(x->a) f(x)`

The significance of this is that, most functions have both right-hand-limit and left-hand-limit equal.

When left-hand-limit and right-hand-limit are equal, the limits are referred together as *limit of a function*.

** Limit of a function: ** Given function `f(x)` and that `f(x)|_(x=a) = 0/0`.

If `lim_(x->a+) f(x) = lim_(x->a-) f(x)`,

then the common value is referred as limit of the function `lim_(x->a) f(x)`.

*Solved Exercise Problem: *

If a function `f(x)` is discontinuous at `x=a`, then what is `lim_(x->a) f(x)`?

- left-hand-limit
- right-hand-limit
- `f(a)`
- cannot be computed
- cannot be computed

The answer is 'cannot be computed'. It is given that the function is discontinuous at `x=a`, and that implies left-hand-limit and right-hand-limits are not equal. In that case, limit of the function cannot be computed without specifying left or right.

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