Question

How do you find the limit of `((x/4)+3)` as x approaches `6`?

Answer 1

`lim_(x rarr 6) (x/4+3) = 4.5`

Explanation:

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

Consequently

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

hence

`lim_(x rarr 6) (x/4+3) = lim_(x rarr 6) f(x)`
`" " = f(6)`
`" " = 6/4+3`
`" " = 4.5`