Question

lim_{x rightarrow -infty} ((1-2x^2-x^4)/(5+x-3x^4))

Answer 1

guess my last answer was not clear

Answer 2

i will try again. you are taking a limit as x goes to minus infinity.

in this case you have a rational function, meaning one polynomial over another. the degrees of both polynomials are the same, and that is all that matters.

since the degrees are equal, you take the ratio of the leading coefficients.

the leading coefficient of the numerator is -1 (that is the coefficient of the term of degree 4) and the leading coefficient of the denominator is -3 and -1/-3= 1/3

Answer 3

\[\lim_{x \rightarrow \infty } (1-2x^2-x^4)/(5+x-3x^4)\]
if we have limit x---> infinity then 1/x ---> 0 and so 1/x^n--->infinity if n>=1

Answer 4

we'll try to create 1/x^n in the given polynomial so we can replace them by zero
divide both numerator and denominator by x^4( highest power of x in denominator)
we'll get
\[\lim_{x \rightarrow \infty} (1/x^4-2/x^2-1)/(5/x^4+1/x^3-3)\]
REPLACE 1/x, 1/x^2, 1/x^4,1/x^3 by 0
the left part is -1/-3 or 1/3
this is the solution