{
"query": {
"display": "$$\\lim_{x\\to\\:\\infty\\:}\\left(x^{8}\\right)$$",
"symbolab_question": "BIG_OPERATOR#\\lim _{x\\to \\infty }(x^{8})"
},
"solution": {
"level": "PERFORMED",
"subject": "Calculus",
"topic": "Limits",
"subTopic": "SingleVar",
"default": "\\infty ",
"meta": {
"showVerify": true
}
},
"steps": {
"type": "interim",
"title": "$$\\lim_{x\\to\\:\\infty\\:}\\left(x^{8}\\right)=\\infty\\:$$",
"input": "\\lim_{x\\to\\:\\infty\\:}\\left(x^{8}\\right)",
"steps": [
{
"type": "step",
"primary": "Apply Infinity Property: $$\\lim_{x\\to\\pm\\infty}\\left(ax^{n}+\\cdots+bx+c\\right)=\\infty,\\:a>0,\\:$$n is even<br/>$$a=1,\\:n=8$$",
"result": "=\\infty\\:"
}
],
"meta": {
"solvingClass": "Limits",
"practiceLink": "/practice/limits-practice",
"practiceTopic": "Limits"
}
},
"plot_output": {
"meta": {
"plotInfo": {
"variable": "x",
"plotRequest": "yes"
},
"showViewLarger": true
}
},
"meta": {
"showVerify": true
}
}
Solution
Solution
Solution steps
Apply Infinity Property: n is even
Graph
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Frequently Asked Questions (FAQ)
What is the limit as x approaches infinity of x^8 ?
The limit as x approaches infinity of x^8 is infinity