1. By considering different paths of approach, show that the function has no limit as (x, y) > (0, 0).
f(x, y) = - x / √ x^2 + y^2
2. Find the limit as (x, y) > (0, 0) along the path y = x for x > 0.

1. shown below

2.

Step-by-step explanation:

We say exists if the limit remains the same along every path.

Here, f is a function on two variables defined on a disk that contains the point (a,b).

1.

Along y-axis i.e., x = 0:

Along x-axis i.e., y = 0:

As the limit is not the same along different paths, so limit does not exist.

2.

Along the path x = y:

the inequality is:

250c+180g≥950

step-by-step explanation:

let c denotes the number of days in a week   miyoko worked as a cryptographer.

and g denotes the number of days in a week she works as a geologist.

now we are given that she earns $250 for every day she works as a cryptographer,and earns $180 for every day she works as a geologist.

now miyoko's goal is to earn more than $950 this week.

hence, the inequality could be represented as:

250c+180g≥950