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#1 2006-11-09 10:23:59

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

Help me....Limits without using 'L' Hospital's rule

(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 up


Letter, number, arts and science
of living kinds, both are the eyes.

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#2 2006-11-09 10:28:18

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

Re: Help me....Limits without using 'L' Hospital's rule

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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#3 2006-11-09 23:39:02

gnitsuk
Member
Registered: 2006-02-09
Posts: 118

Re: Help me....Limits without using 'L' Hospital's rule

a)

Which as x -> ∞ is clearly 2

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#4 2006-11-09 23:45:40

gnitsuk
Member
Registered: 2006-02-09
Posts: 118

Re: Help me....Limits without using 'L' Hospital's rule

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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#5 2006-11-09 23:57:01

gnitsuk
Member
Registered: 2006-02-09
Posts: 118

Re: Help me....Limits without using 'L' Hospital's rule

1)

is as x->∞ clearly equal to zero.

But if you meant

Then the limit as x->∞ is clearly 1

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#6 2006-11-09 23:58:02

gnitsuk
Member
Registered: 2006-02-09
Posts: 118

Re: Help me....Limits without using 'L' Hospital's rule

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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