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(a) Evluate lim {2^x^2-cos^2 (x)}/x^2
x->∞
b) lim sin^(-1) x/x
x->0
For each of the following, either find the limit or state that "no limit exists" and briefly explain
why. Show work used to get your answer.
1. lim (2+3sinx)/x^3+1
x->∞
2. lim cos x
x->∞
Thanks in Advance
Letter, number, arts and science
of living kinds, both are the eyes.
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Good question. Keep posting such types of questions. Let me also try this. Hope to get the answer soon. All the best.
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a)
Which as x -> ∞ is clearly 2
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b)
which as x -> 0 is clearly equal to +∞ as if x is infinetesimally small and positive then so is sin(x) and if x is infinetesimally small and negative then so too in sin(x) and so limit is always +∞.
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1)
is as x->∞ clearly equal to zero.
But if you meant
Then the limit as x->∞ is clearly 1
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2)
is undefined as cos varies continually between -1 and 1 as x increases without limit.
Last edited by gnitsuk (2006-11-09 23:59:03)
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