to infinity and a certain number

Calculus Level 1

Solve the following limit of a function that tends to infinity.

lim ⁡ x → ∞ 7 x 3 − 6 x 2 + 25 x − 5 x 3 \lim_{x\to\infty} \frac{7x^3-6x^2+25}{x-5x^3}


The answer is -1.4.

Dominic Parnell by dominic parnell , 25, United Kingdom

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2 solutions

Mita Ramabulana
Dec 4, 2015

The terms with the highest powers in the numerator and denominator will dominate. So you can consider the terms with the highest power and ignore the rest. That leaves you with a fraction of cubic terms, cancel out and find the limit of the number.

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Dominic Parnell
Nov 23, 2015

1.) Factor out x^3 from both the denominator and numerator. 2.) See what cancels out when it tends to infinity (N.B. x^3 's will cancel out) 3.) The final fraction left will be: \frac{7}{-5} = -1.4

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