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Subject: trig limits I was wondering if it was possible to find: lim x-->infinity cos x Using large numbers don't work on my calculator, and shouldn't it need to be a real number to fall somewhere on the oscillation, rather than somewhere in [-1,1]?
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Hi there. As x grows large, cos x just continues to oscillate in [-1,1], so this limit is undefined. Remember that cos x is like the height of a stone in the tread of a tire, varying between [-r,r] above/below the axle. As the wheel turns and x increases, cos x (the height of the stone above the axle) changes and varies. So if the wheel keeps going on to infinity, the stone keeps moving up and down and never settles on any single height. This is the real-world example that shows why the limit is undefined in this case. Hope this helps, |
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