How do you find the limit of #(1-2x^2-x^4)/(5+x-3x^4)# as #x->-oo#?

Answer 1

The limit is #y=1/3#

Rearranging the terms of the expression

#(1-2x^2-x^4)/(5+x-3x^2)=(-x^4-2x^2+1)/(-3x^4+x+5)# As both numerator and denominator are polynomials, we take the highest degree limit#=(-x^4)/(-3x^4)=1/3# #x->-oo# graph{(y-(-x^4-2x^2+1)/(-3x^4+x+5))(y-1/3)=0 [-5.546, 5.55, -2.77, 2.777]}
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Answer 2

To find the limit of the given expression as x approaches negative infinity, we can focus on the highest power of x in the numerator and denominator. In this case, it is x^4.

By dividing both the numerator and denominator by x^4, we get:

(1/x^4 - 2/x^2 - 1)/(5/x^4 + x^-3 - 3)

As x approaches negative infinity, the terms with positive powers of x (1/x^4 and 5/x^4) tend to zero. The term x^-3 also tends to zero since x is approaching negative infinity.

Thus, the limit simplifies to:

(-1)/(0 - 3)

Which is equal to:

1/3

Therefore, the limit of the given expression as x approaches negative infinity is 1/3.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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