Question
Asked Oct 10, 2019
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We would like to learn HOW to do these type of problems, finding the limits by rationalizing the numerator.  I don't understand.  See #19, #23, #25 and #27.  Please help with as many as you can, thanks!

19. lim + 2
x-2 x+ 8
0uent
3
gotwellor
21. lim V9 +h -3
h0
1
3
ooust ah
x
23. lim
x3 x3
2
25. lim
1 0
t
n
sign
Kom 5
12DXO O
4 Vx
27. lim
16 16x-x2
-Im
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19. lim + 2 x-2 x+ 8 0uent 3 gotwellor 21. lim V9 +h -3 h0 1 3 ooust ah x 23. lim x3 x3 2 25. lim 1 0 t n sign Kom 5 12DXO O 4 Vx 27. lim 16 16x-x2 -Im

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Expert Answer

Step 1

We’ll answer the first question since the exact one wasn’t specified.

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Given:

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lim +2 x-2 8

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Step 2

Identity used is given below:

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Identity: (a +b)(a+b)(a -ab + b)

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Step 3

So now from the given...

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(x + 2) lim x+2 lim x-2 8 = (2)) x2 (x+2) x+2 lim x2 8 By Identity.] lim (x2x-2x + (x+2) x+2 lim x2 8 lim x2 (x2)x -2x+ 4 x +2 lim 1 lim (r-2x+ x-2 x +2 lim 3 X2 8 1 By Applying the limits.] [(-2)-2x(-2)+4 x +2 lim 1 [4+4+4] x +2 lim X2 x8 1 12

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Tagged in

Math

Calculus

Limits