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**Prakash Panneer****Member**- Registered: 2006-06-01
- Posts: 110

(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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**Joel****Member**- Registered: 2006-11-09
- Posts: 5

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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**gnitsuk****Member**- Registered: 2006-02-09
- Posts: 121

a)

Which as x -> ∞ is clearly 2

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**gnitsuk****Member**- Registered: 2006-02-09
- Posts: 121

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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**gnitsuk****Member**- Registered: 2006-02-09
- Posts: 121

1)

is as x->∞ clearly equal to zero.

But if you meant

Then the limit as x->∞ is clearly 1

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**gnitsuk****Member**- Registered: 2006-02-09
- Posts: 121

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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