Question

http://screencast.com/t/HcRi9EvunMQj

Can you help me solve the limit? :)

EDIT: f(x) = 7 g(x) = - 6

Answer 1

what is f(x) and g(x)

Answer 2

I am sorry I totally forgot f(x) = 7 g(x) = - 6

Answer 3

so our equation would be \[\lim_{x \rightarrow -infty} \frac{ 7x }{ -6(2x+3) }\]

Answer 4

correct?

Answer 5

yes

Answer 6

getting -6 inside our equation would be \[\frac{ 7x }{ -12x-18 }\]

Answer 7

do u know the shortcuts finding limits?

Answer 8

I am sorry no

Answer 9

for infinite limits
(1) if numerator's exponent value is greater then limit approaches infinity
(2) if denominator's exponent value is greater then limit approaches zero
(3) if both numerator and denominator's exponent value are same then limit is the coefficient of highest term in numerator divided by coefficient of highest term in denominator

Answer 10

so which rule we wud use here?

Answer 11

hmm sec

Answer 12

bad guess...read the rules and tell me

Answer 13

rule number 3?

Answer 14

@Best_Mathematician

Answer 15

u got it why r we using it

Answer 16

because both exponents in every term are 1

Answer 17

correct so what wud be the answer as per rule # 3

Answer 18

-infinity/infinity

Answer 19

uggh no...what is coefficient of x in numerator and denominator

Answer 20

This may sound stupid, but what do you mean by "coefficient" ? :S

Answer 21

if we have 3x^2 coefficient is 3

Answer 22

oh

Answer 23

so u still gotta answer my question

Answer 24

hurry lol i m sleepy its 12:30 here

Answer 25

so it would be (xf(x))/((2x+3)g(x))

Answer 26

oooih highest term sec

Answer 27

x/(2x+3)

Answer 28

what r coefficient in 7x/(-12x-18)

Answer 29

(7x)/1

Answer 30

coefficient of just x ignore rest of stuff

Answer 31

its 7

Answer 32

and whts in denominator

Answer 33

@dumbcow what are the coefficients in 7x/(-12x-18)

Answer 34

the coefficients of "x" are 7 and -12

\[\lim_{x \rightarrow \infty}\frac{7x}{-12x-18} = \lim_{x \rightarrow \infty} \frac{\frac{7x}{x}}{\frac{-12x}{x}-\frac{18}{x}} = \lim_{x \rightarrow \infty}\frac{7}{-12-\frac{18}{x}}\]
and
\[\lim_{x \rightarrow \infty}\frac{a}{x} = 0\]
thus
\[\lim_{x \rightarrow \infty}\frac{7x}{-12x-18} = -\frac{7}{12}\]