I am having trouble with showing by definition that limits exist. For example limit as x goes to 3 for 5(x^2)-17(adsbygoogle = window.adsbygoogle || []).push({});

3-D < x < 3+D

28-E < 5x^2 - 17 < 28+E

45-E < 5x^2 < 45+E

9-E/5 < x^2 < 9+E/5

sqrRoot(9-E/5) < x < sqrRoot(9+E/5)

so does it mean that 3-D=sqrRoot(9-E/5) ?

then D=3+-sqrRoot(9-E/5)? If it is correct, can you do it without knowing the limit?

In linear equation you can solve it without even knowing the limit:

lim x goes to 3 for 5x - 17

3-D < x < 3+D

L=limit (5*3-17=-2)

L-E < 5x - 17 < L+E

L+17-E < 5x < L+17+E

(L+17)/5 - E/5 < x < (L+17)/5 + E/5

(L+17)/5=3

L+17=15

L=-2

3- E/5 < x < 3+ E/5

So D=E/5

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# Homework Help: Showing by definition that limits exist

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