Student[Calculus1] - Maple Programming Help

Home : Support : Online Help : Education : Student Packages : Calculus 1 : General : Special Points : Student/Calculus1/Roots

Student[Calculus1]

 Roots
 find the real roots (zeros) of an expression

 Calling Sequence Roots(f(x), x, opts) Roots(f(x), x = a..b, opts) Roots(f(x), a..b, opts)

Parameters

 f(x) - algebraic expression or equation in variable 'x' x - name; specify the independent variable a, b - algebraic expressions; specify restricted interval for roots opts - equation(s) of the form numeric=true or false; specify computation options

Description

 • The Roots(f(x), x) command, where f(x) is an algebraic expression, returns as a list of values points where f(x) is zero.
 • The Roots(f(x), x = a..b) command, where f(x) is an algebraic expression, returns as a list of values points where f(x) is zero in the interval [a,b].
 • If f(x) is an equation, this routine finds the roots of the expression $\mathrm{lhs}\left(f\left(x\right)\right)-\mathrm{rhs}\left(f\left(x\right)\right)$, in the specified interval if one is provided.
 • If the independent variable can be uniquely determined from the expression, the parameter x need not be included in the calling sequence.
 • A root (or zero) of f(x) is defined as any point at which the value of the expression f(x) is $0$ (zero).
 • If the expression has an infinite number of roots, a warning message and sample roots are returned.
 • The opts argument can contain the following equation that sets computation options.
 numeric = true or false
 Whether to use numeric methods (using floating-point computations) to find the roots of the expression. If this option is set to true, the points a and b must be finite and are set to $-10$ and $10$ if they are not provided. The default value of this option is determined by the numeric values in the expression $f\left(x\right)$: If any of these numeric values is a floating point number (has a decimal point), then this option defaults to to true.  Note: If the numeric option is in effect, then the command does not warn about an infinite number of roots.

Examples

 > $\mathrm{with}\left(\mathrm{Student}\left[\mathrm{Calculus1}\right]\right):$
 > $\mathrm{Roots}\left(3{x}^{2}-x,x\right)$
 $\left[{0}{,}\frac{{1}}{{3}}\right]$ (1)
 > $\mathrm{Roots}\left(\mathrm{sin}\left(x\right),0..10\right)$
 $\left[{0}{,}{\mathrm{\pi }}{,}{2}{}{\mathrm{\pi }}{,}{3}{}{\mathrm{\pi }}\right]$ (2)
 > $\mathrm{Roots}\left(\mathrm{sin}\left(\frac{1.0}{x}\right),-1..1\right)$
 $\left[{-0.3183098862}{,}{-0.1591549431}{,}{-0.1061032954}{,}{-0.07957747155}{,}{-0.06366197724}{,}{-0.05305164770}{,}{-0.03978873577}{,}{-0.02448537586}{,}{-0.009947183943}{,}{0.004973591972}{,}{0.01989436789}{,}{0.03536776513}{,}{0.05305164770}{,}{0.06366197724}{,}{0.07957747155}{,}{0.1061032954}{,}{0.1591549431}{,}{0.3183098862}\right]$ (3)
 > $\mathrm{Roots}\left(2{x}^{3}+5{x}^{2}=4x,x\right)$
 $\left[{-}\frac{{5}}{{4}}{-}\frac{\sqrt{{57}}}{{4}}{,}{0}{,}{-}\frac{{5}}{{4}}{+}\frac{\sqrt{{57}}}{{4}}\right]$ (4)
 > $\mathrm{Roots}\left(\frac{{x}^{2}-3x+1}{x}\right)$
 $\left[\frac{{3}}{{2}}{-}\frac{\sqrt{{5}}}{{2}}{,}\frac{{3}}{{2}}{+}\frac{\sqrt{{5}}}{{2}}\right]$ (5)
 > $\mathrm{Roots}\left(\frac{{x}^{2}-3x+1}{x}=0,\mathrm{numeric}\right)$
 $\left[{0.3819660113}{,}{2.618033989}\right]$ (6)
{"ft_lang_label":"__label__en","ft_lang_prob":0.6752139,"math_prob":0.99994206,"size":2641,"snap":"2020-45-2020-50","text_gpt3_token_len":830,"char_repetition_ratio":0.13462268,"word_repetition_ratio":0.076246336,"special_character_ratio":0.32374102,"punctuation_ratio":0.17574692,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9997762,"pos_list":[0,1,2],"im_url_duplicate_count":[null,null,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2020-12-03T13:42:41Z\",\"WARC-Record-ID\":\"<urn:uuid:06c893cf-0958-405e-9902-416817659208>\",\"Content-Length\":\"237859\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:fc758e53-fff2-479e-b525-89cc6dfec476>\",\"WARC-Concurrent-To\":\"<urn:uuid:930d9906-47a4-412c-b40d-b2318ad5e022>\",\"WARC-IP-Address\":\"199.71.183.28\",\"WARC-Target-URI\":\"https://de.maplesoft.com/support/help/maple/view.aspx?path=Student%2FCalculus1%2FRoots\",\"WARC-Payload-Digest\":\"sha1:ZTFH6G2FNGEVWIYT3HJEM5NUB5R7JZDV\",\"WARC-Block-Digest\":\"sha1:4QQJYE2M5LCRBNYGX7EHHD7HACXYWWUJ\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2020/CC-MAIN-2020-50/CC-MAIN-2020-50_segments_1606141727782.88_warc_CC-MAIN-20201203124807-20201203154807-00243.warc.gz\"}"}