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romanna [79]
2 years ago
8

Need to show work for limits

Mathematics
1 answer:
Sergeu [11.5K]2 years ago
3 0

Answer:

\displaystyle \lim_{x \to -\infty} (-7x^5 + x^3) = \infty

General Formulas and Concepts:
<u>Calculus</u>

Limits

Limit Rule [Variable Direct Substitution]:
\displaystyle \lim_{x \to c} x = c

Step-by-step explanation:

<u>Step 1: Define</u>

<em>Identify given.</em>

<em />\displaystyle \lim_{x \to -\infty} (-7x^5 + x^3)

<u>Step 2: Evaluate</u>

  1. [Limit] Apply Limit Rule [Variable Direct Substitution]:
    \displaystyle \lim_{x \to -\infty} (-7x^5 + x^3) = -7(- \infty)^5 + (- \infty)^3

Recall that x⁵ is a "faster" function than x³. Also recall that we have 2 negatives, which would turn <em>positive</em>. Therefore, we can <em>ignore </em>the 2nd part of the limit and focus on the first:
\displaystyle \begin{aligned}\lim_{x \to -\infty} (-7x^5 + x^3) & = -7(- \infty)^5 + (- \infty)^3 \\& = -7(- \infty)^5 \\& = -7(- \infty) \\& = 7(\infty) \\& = \boxed{\infty} \\\end{aligned}

∴ we have found the limit to equal infinity.

---

Learn more about limits: brainly.com/question/27438198

Learn more about calculus: brainly.com/question/27351658

---

Topic: AP Calculus AB/BC (Calculus I/I + II)

Unit: Limits

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