Find the limit. Find the limit.-4x+2lim7x²+4a. 1b. 01с.4d.-e.

We have to find the limx→∞−4x+27x2+4 If we substitute the limit, then it is of the form ∞∞ Apply…

Answered: Find the limit. -4x+2 lim x- o 7x2+4 a.…

PREALGEBRA

15th Edition

ISBN:9781938168994

Author:OpenStax

Publisher:OpenStax

Chapter11: Graphs

Section11.4: Understand Slope Of A Line

Problem 11.73TI: Find the slpoe of the line: y=7

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Find the limit.

Expert Solution

Step 1

We have to find the $\lim_{x \to \infty} \frac{- 4 x + 2}{7 x^{2} + 4}$

If we substitute the limit, then it is of the form $\frac{\infty}{\infty}$

Apply L'Hospital rule $\lim_{x \to c} \frac{f (x)}{g (x)} = \frac{\lim_{x \to c} f^{'} (x)}{\lim_{x \to c} g^{'} (x)}$

Hence,

$\begin{matrix} \lim_{x \to \infty} \frac{- 4 x + 2}{7 x^{2} + 4} = \lim_{x \to \infty} \frac{- 4 \cdot 1 + 0}{7 \cdot 2 x + 0} \\ = \lim_{x \to \infty} \frac{- 4}{14 x} \\ = \lim_{x \to \infty} \frac{- 2}{7 x} \end{matrix}$

Hence, $\lim_{x \to \infty} \frac{- 4 x + 2}{7 x^{2} + 4} = \lim_{x \to \infty} \frac{- 2}{7 x}$

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