Question
Asked Nov 8, 2019
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Compute the following limit using l'HWopital's rule if appropriate. Use INF to denote oo and MINF to denote -oo.
x3 8x2 - x) =
xoo
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Compute the following limit using l'HWopital's rule if appropriate. Use INF to denote oo and MINF to denote -oo. x3 8x2 - x) = xoo

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Expert Answer

Step 1

Now,

8x2
lim Vx3
хэ0о
We know that,
а3 — Ь3 — (а —b) (а? + ab + b2)
So. (-8x2)
1
8x2)-x) ((x3-8x2)f+x(x3 - 8x2)3 + x
х
3
1
-x3
(х3.
- 8x
(x-8x2)-x =
2
1
(x3-8x2)3+x(x3-8x2)3+x2
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8x2 lim Vx3 хэ0о We know that, а3 — Ь3 — (а —b) (а? + ab + b2) So. (-8x2) 1 8x2)-x) ((x3-8x2)f+x(x3 - 8x2)3 + x х 3 1 -x3 (х3. - 8x (x-8x2)-x = 2 1 (x3-8x2)3+x(x3-8x2)3+x2

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Step 2

Now,

lim Vx3-8x2- x)
lim 38x2 x)
хсо
3
(x3_8x2)) -12
lim
1
((x3-8x2)3+x(x3-8x2)3+x2
х—со
х3-8х2—х3
lim
1
2
(x3-8x2)3+x(x3-8x2)3+x2)
х-со
-8x2
lim
1
(x3-8x2)3+x(x3-8x2)3+x2
х-со
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lim Vx3-8x2- x) lim 38x2 x) хсо 3 (x3_8x2)) -12 lim 1 ((x3-8x2)3+x(x3-8x2)3+x2 х—со х3-8х2—х3 lim 1 2 (x3-8x2)3+x(x3-8x2)3+x2) х-со -8x2 lim 1 (x3-8x2)3+x(x3-8x2)3+x2 х-со

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Step 3

Further calcu...

-8x2
= lim
)
1
хэсо
х2
8 3
+1
-8
lim
8 3
хсо
E8
+1
х,
-8
1
((1-0)3+(1-0)š+1
-8
8
(1+1+1)
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-8x2 = lim ) 1 хэсо х2 8 3 +1 -8 lim 8 3 хсо E8 +1 х, -8 1 ((1-0)3+(1-0)š+1 -8 8 (1+1+1)

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Math

Calculus