Question

How do you find the limit of `3x^3-2x^2+4` as `x->1`?

Answer 1

`lim_(x rarr 1) (3x^3-2x^2+4) = 5`

Explanation:

If we define `f(x)=3x^3-2x^2+4`, then `f(x)` is continuous everywhere (ie it is well behaved and it has no jumps, discontinuities or places where the function is not defined).

Consequently

`lim_(x rarr a) f(x) = f(a)` for all values of `a`

hence

`lim_(x rarr 1) (3x^3-2x^2+4) = lim_(x rarr 1) f(x)`
`" " = f(1)`
`" " = 3-2+4`
`" " = 5`