True or False:
All even functions are continuous everywhere.
If -1 (is less than or equal to) g(x) (is less than or equal to) for all x, then limit as approaches infinity of g(x)=0
I think the first one may be false and the second one is false too
Stacey Warren - Expert brainly.com
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You are right, but the second one didn't really make much sense as you wrote it down. An example of an even function that is discontinuous is this one:
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You're right, I have looked at too many computer plots.
The second one doesn't make much sense since you've missed out a bit:
\[-1 \le g(x) \leq \ ???\]Not that it really matters. I'm fairly sure it's false. You can always pick g(x) = -1, which will always converge to -1, not 0.
(As a technically, we're assuming the upper bound allows such a function \(g\) to exist...)
Not sure what you mean by I have missed a bit. So is the first one true and the secon one false?
The first one is false: there's a counterexample above.
The second one: you said, "If -1 (is less than or equal to) g(x) (is less than or equal to) for all x". But g(x) (is less than or equal to) what?
Although I did point out that it didn't really matter. The second one is also false.
That example isnt a function though since it doesnt meet the vert line test. I typed exactly what was on the question. For all x
You cannot say "g(x) is less than or equal to for all x". Remember maths should be written in English - if you read a sentence and it makes no sense in English, it probably makes no sense. You need to say what g(x) is less than for all x.
Perhaps you mean \(g(x) \leq x\) for all \(x\)?
As for the first question, satellite removed the offending vertical lines.
So this is a valid even and discontinuous function. (The black dots represent a point that is included in the function, while the white dots represent a point not included. You can see this now satisfies the vertical line test.)
ah I see my mistake, it is less than or equal to 1 for all x
thanks, too bad I can't give two ppl best answers :P