Question

What is the value of the following limit: `lim_(x-> 1) (1/(x + 3) - 1/(1 + 3))/(x - 1)`?

Answer 1

`-1/16`, or choice A.

Explanation:

The notation `f(x)` signifies to put the function into the limit, so:

`=>lim_(x-> 1) (1/(x + 3) - 1/(1 + 3))/(x - 1)`

`=> lim_(x-> 1) ((4 - 1(x + 3))/(4(x + 3)))/( x - 1)`

`=> lim_(x-> 1) ((4 - x - 3)/(4(x + 3)))/(x- 1)`

`=> lim_(x-> 1) ((1 - x)/(4(x +3)))/(x- 1)`

`=> lim_(x-> 1) (1 - x)/(4(x + 3)(x - 1))`

`=> lim_(x->1) -(x -1)/(4(x + 3)(x - 1))`

`=> lim_(x->1) -1/(4(x + 3))`

We can evaluate now:

`=> -1/(4(1 + 3))`

`=> -1/16`

This would be choice A.

Hopefully this helps!