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Log(2 + sin2x) (x 4 + x 2 + 1)e sinx > 0 true or false?

Log(2 + sin2x) (x4 + x2 + 1)esinx > 0
true or false?

Grade:12th Pass

1 Answers

Swapnil Saxena
102 Points
9 years ago

For this situatiuon , It is always either greater than 0 or equal to 0 because

Log(2+sin(2x)) ==> the least value that the sin (2x) can take is (-1) which will make the function log(1)=0.So the least value of this function is 0. So Log(2+sin(2x)) will always take positive values


(x4+x2+1) ==> It is quite evident that (x4+x2+1)  can never take negative values because x4 and x2 always take positive values for all x


esin(x) ==> The least value that this function can take when sin(x) is -1 = (1/e) which is also a positive quantity.

So If all the individual functions always return positive quantities Then the function can neer take negative values so it must be >0

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