Let f : (0, 1) → R be a continuous function such that limx→0 f(x) = limx→1 f(x) = 0. Show that f achieves either an absolute minimum or an absolute maximum on (0, 1) (but perhaps not both).
Hint: A picture could help. One might also think "too bad the function isn’t defined and continuous in all of [0, 1], then we could apply the min-max theorem." However, isn’t that easily remedied?
Solution. I will give two solutions. The second solution, slightly modified, can used to prove that the same result holds if f : R → Ris continuous and limx→±[infinity] f(x) = 0.

answer:  

step-by-step explanation:

odd numbers are only divisible by 1 and itself.

even numbers are divisible by more than 1 and itself.

for example 6 is even because it is divisible by more than 1 and its self. 1 x 6= 6 ; 2 x 3= 6

and 7 is odd because only 7 x 1 equals seveb

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we can set up an equation to find the girls' ages. the equation is         28=0.5x-5+x. (comment if you need me to explain how i got this equation.) so, you add x and 0.5x to get 1.5x and add 5 to each side. your new equation is 33=1.5x. now divide both sides of the equation by 1.5 to get 22=x. because x is mary's age, to find jasmine's age we subtract mary's age from 28. we find that mary is 22 years old and jasmine is 6 years old.