Help would be very much appreciated please

  • Thread starter bballj228
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  • #1
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Evaluate the limit and indicate appropriate limit laws.

lim square root of u^4+3u+6
u->-2

Evaluate the limit

lim x^2+5x+4/x^2-3x-4
x->-4

Find the limit

lim t^2+2/t^3+t^2-1
t->-infinity

Please can someone help me?
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  • #2
arildno
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Well, let's take the first one, inserting -2 at the u's place, we get 16=2^4.

Thus, we may check whether 16 is, indeed, the limit as u tends to -2.

We therefore manipulate the expression:
[tex]|u^{4}+3u+6-16|=|(u^{4}-2^{4}+3(u+2)|=|(u^{2}+2^{2})(u-2)(u+2)+3(u+2)|=|u+2||(u^{2}+4)(u-2)|[/tex].
Thus, if you can argue for that the latter factor is bounded as u tends to -2, the factor |u+2| will ensure that the entire expression tends to zero, proving that 16, indeed, is the limit of the given expression.
 

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