Question

(i.)lim x→60- f(x) (ii.) lim x→60+ f(x) (iii.) What can you conclude about lim x→60 f(x)? How is this shown by the graph? (iv.) What aspect of costs of renting a car causes the graph to jump vertically by the same amount at its discontinuities? 

(refer to image)

Answer 1

See below.

Explanation:

1. The expression `\lim_{x\to 60^-}` means to take the limit as `x` approaches `60`, but only coming from values smaller than `60`. So, if you imagine to walk along the `x` axis towards the `60` marker, coming from left, you can see that the function evaluates to `56`.
2. Same as above, except this time you come from right. So, the answer is 68.
3. The limit is not defined. In fact, `\lim_{x\to 60}` is defined if and only if `\lim_{x\to 60^-}` and `\lim_{x\to 60^+}` both exist and are the same. In this case they both exist, but they differ. This can be deduced by looking at the graph because it has jumps.
4. Not sure about what this question is asking, but if I'm right, the jumps in the graph mean that if you rent the car for max `20` minutes, it will cost you 32 dollars. If instead you rent the car for any amount of time between 21 and 40 minutes, it will cost you `44` dollars, and so on.