Question

If f and g are continous functions and f(x) _> 0 for all real numbers x, which of the following must be true?

Answer 1

@AccessDenied @johnweldon1993

Answer 2

second one

Answer 3

@sourwing how do you know?

Answer 4

There can be more than one answer.

Answer 5

There are counterexamples for 1 and 3

Answer 6

\[\int\limits_{0}^{1} \sqrt{x} (-x^2) dx \ne (∫_{0}^{1} \sqrt{x}\ dx ) (\int\limits_{0}^{1} (-x^2)\ dx\]

Answer 7

Is that the only correct answer then?

Answer 8

\[\int\limits_{0}^{1} \sqrt{x}\ dx \ne\sqrt{\int\limits_{0}^{1} x\ dx}\ dx\]

Answer 9

so ii is the only correct answer

Answer 10

integral of the sum is the sum of integrals

Answer 11

thank you! lol, are you a current college student?

Answer 12

no

Answer 13

oh, I see. Thanks for your help!