Compute [math: limx→−∞x7]\displaystyle \lim _{x o -\infty }{x^7}. (Use I to stand for [math: ∞]\infty if needed.)

Question

Compute [math: limx→−∞x7]\displaystyle \lim _{x	o -\infty }{x^7}. (Use I to stand for [math: ∞]\infty if needed.)

BlackTom AI · Accepted Answer

We are evaluating the limit as x approaches negative infinity of x^7.

First, recall that raising x to an odd power preserves the sign of x: if x is negative, x^7 remains negative, and as |x| grows larger, |x^7| grows without bound.

Second, consider the behavior as x decreases without bound (x → -∞). Since x is negative and its magnitude |x| increases without bound, x^7 = x · x · x · x · x · x · x will multiply negative numbers together seven times, resulting in increasingly large negative values.

Therefore, the function x^7 tends to negative infinity as x tends to negative infinity, because the magnitude grows without limit while the sign stays negative.

Note on notation: writing -∞ conveys the direction of the unbounded decrease. If one were to imagine infinity in the opposite direction, ∞ would imply unbounded growth in the positive direction, which does not describe this limit since the seventh power of a large negative x remains negative.

In summary, the limit diverges to negative infinity due to the odd power and the unbounded decrease of x.

_MATH1013_1ABCD_2025 Subsection 3.2 (closed on 4 Oct)

Compute [math: limx→−∞x7]\displaystyle \lim _{x\to -\infty }{x^7}. (Use I to stand for [math: ∞]\infty if needed.)

View Explanation

Log in for full answers

Similar Questions

Compute \(\displaystyle \lim _{x\to -\infty }{\frac {x^4-8x^3-3x+5}{6x^4+7x^2+3}}\). (Use I to stand for \(\infty \) if needed.)

Compute [math: limx→−∞x4−8x3−3x+56x4+7x2+3]\displaystyle \lim _{x\to -\infty }{\frac {x^4-8x^3-3x+5}{6x^4+7x^2+3}}. (Use I to stand for [math: ∞]\infty if needed.)

Compute [math: limx→−∞−4x3+2x2+6x−57x4+4x2+1]\displaystyle \lim _{x\to -\infty }{\frac {-4x^3+2x^2+6x-5}{7x^4+4x^2+1}}. (Use I to stand for [math: ∞]\infty if needed.)

Compute \(\displaystyle \lim _{x\to -\infty }{\frac {3x^4-4x^3-2x+1}{8x^4+9x^2+5}}\). (Use I to stand for \(\infty \) if needed.)

Compute [math: limx→−∞3x4−4x3−2x+18x4+9x2+5]\displaystyle \lim _{x\to -\infty }{\frac {3x^4-4x^3-2x+1}{8x^4+9x^2+5}}. (Use I to stand for [math: ∞]\infty if needed.)

Compute limx→−∞x13[math]\displaystyle \lim _{x\to -\infty }{x^{\frac {1}{3}}}. (Use I to stand for ∞[math]\infty if needed.)

More Practical Tools for Students Powered by AI Study Helper

Homework AI Solver

Stylized AI Paper Writer

Plagiarism Checker Assistant

Citation AI Academic Writing Tool

In-Class Translation Assistant

AI Note Generator

AI Quiz Answers

Past Exam Questions from University Test Bank

Smart Practice Assistant

Adaptive Practice

Making Your Study Simpler