Afunction f: r^{^{n}}\rightarrow r^{m} ? is said to be proper if it is continuous and the following implication holds:
for any sequence x? k , \left \| x_{k} \right \|\rightarrow \infty \rightarrow \left \| f(x_{k}) \right \|\rightarrow \infty .
a) give an example of a proper function from r to r.
b) show that a continuous function from r? n to rm ? is proper if and only if inverse image of any compact set is compact.
c) if f: rn \rightarrow ? r is a proper function, show that |f| attains its global minimum on rn.

True or false? a triangle can be circumscribed about a given circle

To convert celsius temperatures to fahrenheit, you can use the expression (c + 32). tom says that another way to write this expression is c + 32. what error did tom make?

Kevin has a spinner that has 10 equal sections and 2 sections of each color—red, blue, green, yellow, and purple. kevin spins the spinner 180 times. kevin determines about how many times the spinner will land on red or green, and his work is shown below. -kevin has the formula reversed; it should be the total number of sections over the number of red or green sections. -kevin should have used a 4 in the numerator because there are 2 red sections and 2 green sections. -kevin should multiply by the number of sections in the spinner rather than the total number of spins. -kevin calculated the prediction correctly and did not make any mistakes.