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calculus: find the limit?
lim as x approaches infiniti of 1 divided by 2x+sinx
I know the answer is 0 but pleeeease explain to me why! I'm so confused!
2 Answers
- EvanLv 61 decade agoFavorite Answer
the sin x on the bottom goes between -1 and 1, 2x gets very big, and ultimately adding + or - 1 on the bottom doesn't matter. More precisely,
1 / (2x - 1) <= 1 / (2x + sin x) <= 1 / (2x + 1)
Since the limit of the left and right items are 0 as x-> infinity, they squeeze the middle one too.
- 1 decade ago
okay, pretend x becomes a really big number
1 is a very small number, so as x gets bigger and bigger, the stop stays at 1 but the bottom becomes 2(big number) + sin(big number)
so its equal to 1/really big number, which gets closer and closer to 0, decimals like .00000000000001 to 0.00000000000000000000001
