# Evaluate limit as x approaches infinity of (10x^3-6x^2-5x)/(4-2x-7x^3)

Take the limit of each term.
Reorder and .
Move .
Reorder and .
Divide the numerator and denominator by the highest power of in the denominator, which is .
Simplify each term.
Cancel the common factor of .
Cancel the common factor.
Divide by .
Cancel the common factor of and .
Factor out of .
Cancel the common factors.
Factor out of .
Cancel the common factor.
Rewrite the expression.
Move the negative in front of the fraction.
Cancel the common factor of and .
Factor out of .
Cancel the common factors.
Factor out of .
Cancel the common factor.
Rewrite the expression.
Move the negative in front of the fraction.
Simplify each term.
Cancel the common factor of .
Cancel the common factor.
Divide by .
Cancel the common factor of and .
Factor out of .
Cancel the common factors.
Factor out of .
Cancel the common factor.
Rewrite the expression.
Move the negative in front of the fraction.
Split the limit using the Limits Quotient Rule on the limit as approaches .
Split the limit using the Sum of Limits Rule on the limit as approaches .
Move the term outside of the limit because it is constant with respect to .
Since its numerator approaches a real number while its denominator is unbounded, the fraction approaches .
Move the term outside of the limit because it is constant with respect to .
Since its numerator approaches a real number while its denominator is unbounded, the fraction approaches .
Split the limit using the Sum of Limits Rule on the limit as approaches .
Move the term outside of the limit because it is constant with respect to .
Since its numerator approaches a real number while its denominator is unbounded, the fraction approaches .
Move the term outside of the limit because it is constant with respect to .
Since its numerator approaches a real number while its denominator is unbounded, the fraction approaches .
Evaluate the limits by plugging in the value for the variable.
Evaluate the limit of which is constant as approaches .
Evaluate the limit of which is constant as approaches .
Simplify the numerator.
Multiply by .
Multiply by .
Simplify the denominator.
Multiply by .
Multiply by .
Move the negative in front of the fraction.
The result can be shown in multiple forms.
Exact Form:
Decimal Form:
Evaluate limit as x approaches infinity of (10x^3-6x^2-5x)/(4-2x-7x^3)

Scroll to top