Question

Evaluate the limit.
limx→0{(3.5+4.5x)^3−42.875}/x=

Answer 1

just plug in x=0

Answer 2

I tried, doesn't it just equal 0/0?

Answer 3

@hartnn

Answer 4

-42.875/0
which is
\(-\infty \)

Answer 5

oops sorry, i misread the question

Answer 6

ok,
so
3.5^3 = 42.875

Answer 7

we have the form of
\(a^3-b^3\)
here
right ?

Answer 8

@hartnn I tried all these already and nothing seems to be working. I've working on this problem for half an hour now, thats why I'm asking on here finally

Answer 9

use the formula
\((a-b)(a^2+ab+b^2)\)
a= 3.5 +4.5 x
b= 3.5

Answer 10

@hartnn so after plugging in the values for a &b I should have the answer?

Answer 11

did you try plugging in?

after that there will be 'x' in the numerator which will get cancelled with the 'x' in the denominator

and then you can directly plug in x=0

Answer 12

so I got : (3.5 - 4.5x)(3.5^2+15.75x+3.5^2)

Answer 13

@hartnn

Answer 14

is that the correct equation?

Answer 15

a-b is just 4.5 x

isn't it ?

Answer 16

you took a = 3.5, b= 4.5x
thats not correct

Answer 17

a= 3.5 +4.5x
b=3.5

Answer 18

ok so then the correct equation is: (4.5x)(3.5^2+15.75x+3.5^2) ?

Answer 19

or (4.5x)(7^2+15.75x)? @hartnn

Answer 20

no...a= 3.5 +4.5x
so a^2 =(3.5 +4.5x)^2

Answer 21

I'm kind of confused now. so if I calculated your equation the answer would be = 23.75? @hartnn

Answer 22

@hartnn nevermind that answer didn't work either

Answer 23

show each of your steps, i'll help u spot the error

Answer 24

okay hold on let me type it out

Answer 25

Formula: (a−b)(a2+ab+b2)
a= 3.5 +4.5 x
b= 3.5

3.5+4.5x - 3.5 = 4.5x

(4.5x)({[3.5+4.5x]*2}+{[3.5+4.5x]*3.5}+[3.5*2])

Answer 26

@hartnn that's the equation I got

Answer 27

ok, thats correct
now cancel out x
and plug in x=0 in the remaining part

Answer 28

the last part is 3.5^2
not 3.5*2

Answer 29

\((4.5x)({[3.5+4.5x]^2}+{[3.5+4.5x]*3.5}+[3.5^2])\)

Answer 30

\((4.5)({[3.5+4.5(0)]^2}+{[3.5+4.5(0)]*3.5}+[3.5^2])\)

Answer 31

@hartnn I might be wrong but so is 70.875 the answer?

Answer 32

using calculator, its 165.375

Answer 33

4.5*3*3.5^2

Answer 34

Yeah that was the correct answer, but how did you get the 4.5*3*3.5^2? I thought the first two parts of the equation equaled 0? so it would be 4.5*3.5+3.5^2

Answer 35

\((4.5)({[3.5+4.5(0)]^2}+{[3.5+4.5(0)]*3.5}+[3.5^2])\)
\((4.5)({[3.5]^2}+{[3.5]*3.5}+[3.5^2]) \\ 4.5 ([3.5^2]+[3.5^2]+[3.5^2])\)

Answer 36

a+a+a=3a

Answer 37

@hartnn oh okay, I see now!

Answer 38

@hartnn thank you so much

Answer 39

welcome ^_^