# Series Help!

• March 29th 2010, 09:14 AM
mathguy123
Series Help!
Find the Maclaurin series of
$f(x)=(1+x^2)^(2/3)$
• March 29th 2010, 11:40 AM
HallsofIvy
f(0)= 1

$f'(x)= (2/3)(x^2+ 1)^{1/3}(2x)= (4/3)x(x^2+ 1)^{1/3}$ so f'(0)= 0.

$f"(x)= (4/3)(x^2+ 1)^{1/3}+ (8/9)x^2(x^+ 1)^{-2/3}$ so f"(0)= 4/3.

Keep going until you see a pattern.
{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 3, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9156570434570312, "perplexity": 21292.028800850625}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 5, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2014-41/segments/1410657123274.33/warc/CC-MAIN-20140914011203-00075-ip-10-196-40-205.us-west-1.compute.internal.warc.gz"}