Question

Evaluate the limit ;

lim x^3/2 - 8 / x-4
x-> 4

Help Please !

Answer 1

6 b on this package http://www.la-citadelle.com/courses/calculus/review01.pdf help please !

Answer 2

Explain the change of base logic please :) !

Answer 3

I know the answer but need explanation the answer is 3 btw

Answer 4

you have the question wronge im sorry can you please go to this link ! and see
i cannot type the question

Answer 5

6b please ! http://www.la-citadelle.com/courses/calculus/review01.pdf

Answer 6

if you want the basic logic: you cannot substitute x = 4 in the denominator because the denominator would then be 0, so you must transform the denominator somehow so its ok to plug x = 4

Answer 7

then....?

Answer 8

try consider x^(3/2) - 8 as
\[(\sqrt{x})^{3}-2^{3}=...\]

Answer 9

Oooh okay .... mind guiding me all the way please :$ ! <333

Answer 10

and x-4 =
\[=(\sqrt{x})^{2}-2^{2}=...\]

I think you can cancel out some terms after that I find your lim

Answer 11

it's some writing... give me few min

Answer 12

okay :)

Answer 13

here we go:
\[=((\sqrt{x})^{3}-2^{3})/((\sqrt{x})^{2}-2^{2})=\]

Answer 14

\[=(\sqrt{x}-2)*((\sqrt{x})^{2}+2\sqrt{x}+4)/(\sqrt{x}-2)(\sqrt{x}+2)=\]

do you see it now?

Answer 15

ooohh difference of cubes. ..

Answer 16

\[(x+2\sqrt{x}+4)/(\sqrt{x}+2)=\]
now get your x->4
you shouldn't have problems any more (no 0/0) :))

Answer 17

omg omg omg yeah i get it :$ thanks hunnie ! <3 can you help me with 6c :$ ! <333 xoxoxoxoxox

Answer 18

http://www.la-citadelle.com/courses/calculus/review01.pdf

Answer 19

yes, lim should be =3
6c?

Answer 20

from here http://www.la-citadelle.com/courses/calculus/review01.pdf

Answer 21

I think that exactly (!) the same approach will work!
Top: \[=(x^{1/6})^{3} - 1^{3}=(x ^{1/6}-1)(x^{2/6}+x ^{1/6}+1)\]

Answer 22

Numerator:
\[(x ^{1/6})^{2} - 1^{2}=...\]
can you finish it?

Answer 23

yess bozzz :) thankyou <3

Answer 24

after "unfolding" & canceling out you'll get (3/2)
Good Luck!

Answer 25

want my number babe :) ?

Answer 26

tehe i jokethanks :)

Answer 27

i was thinking....too long :(
i'll survive :)