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what is the limit of this equation?
x → −infinity
x^3 +1
----------------
x^4 +x +6
2 Answers
- PaulR2Lv 78 years agoFavorite Answer
limit x -> -oo : ( x³ + 1 ) ÷ ( x^4 + x + 6 )
Divide every term by x^4
limit x -> -oo : (( x³ / x^4 )+( 1 / x^4 ))÷(( x^4 / x^4 )+( x / x^4 )+( 6 / x^4 ))
Divide
limit x -> -oo : ( ( 1 / x ) + ( 1 / x^4 ) ) ÷ ( ( 1 ) + ( 1 / x³ ) + ( 6 / x^4 ) )
Plug in -oo
limit x -> -oo : ( ( 1 / -oo ) + ( 1 / -oo ) ) ÷ ( ( 1) + ( 1 / -oo ) + ( 6 / -oo ) )
Remember, usually when you divide by infinity you get zero
limit x -> -oo : ( ( 0 ) + ( 0 ) ) ÷ ( ( 1 ) + ( 0 ) + ( 0 ) )
Add
limit x -> -oo : 0 / 1
Divide
limit x -> -oo : 0
I hope this helps you. Have a good day.
- ?Lv 68 years ago
note that 1/x^n approaches 0 as x approaches +- infinity
Divide the numerator and denominator by x^4
(1/x + 1/x^4)/(1 + 1/x^3 + 6/x^4) as x --> - infinity the quotient approaches 0/1 --> 0
