Question

Question #bc838

Answer 1

We can't, because that is not the limit. If you intended to write `lim_(x->10) 3-(4x)/5 = -5`, then see explanation below.

Explanation:

One of the first steps in checking the limit of a function at an x-value is seeing if the function itself is defined for that value, followed by whether it will be defined for nearby x-values.

In this case our function is:

`(3-4x)/5`

Because this is a simple linear function, it is self evident that the function will be continuous throughout. Thus, the limit shall exist everywhere, and will be equal to the value `f(x_o)` for any `x_0` in the domain.

Knowing this, we plug in `x=10`

`(3-4(10))/5 = (3-40)/5 = -37/5 = -7 2/5 = -7.4`

This is not equal to the `-5` you sought, ergo, `-5` is not the appropriate limit.

It is possible that you mis-wrote the function, but for the function as you have written it, you cannot prove `-5` is the limit because it is not the limit.

If you instead meant to write:

`3-(4x/5)`

You can perform the same process as above. Again, since the function is linear and continuous throughout, the function will be equal to its own limit at any point.

`f(10) = 3 - (4(10))/5 = 3 -40/5 = 3-8 = -5`