# why-sinx-is-not-differentiable-at-x-npi-

Question Number 134519 by sachin1221 last updated on 04/Mar/21
$${why}\:{sinx}\:{is}\:{not}\:{differentiable}\:{at}\:{x}={n}\pi \\$$
Commented by JDamian last updated on 04/Mar/21
seriously?
Answered by physicstutes last updated on 04/Mar/21
$$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\left(\frac{\mathrm{sin}{x}−\mathrm{0}}{{x}−\mathrm{0}}\right)\:=\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{sin}\:{x}}{{x}}\:=\:\mathrm{1} \\$$$$\mathrm{sin}\:{x}\:\mathrm{is}\:\mathrm{also}\:\mathrm{continuous}\:\mathrm{and}\:\mathrm{so}\:\mathrm{it}\:\mathrm{is}\:\mathrm{differentiable}\:\mathrm{at}\: \\$$$$\:{x}\:=\:\mathrm{0}.\:\mathrm{what}\:\mathrm{do}\:\mathrm{you}\:\mathrm{mean}\:\mathrm{by}\:\mathrm{your}\:\mathrm{question}? \\$$
Commented by sachin1221 last updated on 04/Mar/21
$$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\left(\frac{\mathrm{sin}{x}−\mathrm{0}}{{x}−\mathrm{0}}\right)\:=\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{sin}\:{x}}{{x}}\:=\:\mathrm{1} \\$$$$\mathrm{sin}\:{x}\:\mathrm{is}\:\mathrm{also}\:\mathrm{continuous}\:\mathrm{and}\:\mathrm{so}\:\mathrm{it}\:\mathrm{is}\:\mathrm{differentiable}\:\mathrm{at}\: \\$$$$\:{x}\:=\:\mathrm{0}.\:\mathrm{what}\:\mathrm{do}\:\mathrm{you}\:\mathrm{mean}\:\mathrm{by}\:\mathrm{your}\:\mathrm{question}? \\$$$${but}\:{when}\:\boldsymbol{{u}}\:\boldsymbol{{see}}\:\boldsymbol{{graphical}}\:\boldsymbol{{method}}\:\boldsymbol{{at}}\:\boldsymbol{{x}}=\mathrm{0}\:\boldsymbol{{u}}\:\boldsymbol{{will}}\:\boldsymbol{{get}}\:\boldsymbol{{infinite}}\:\boldsymbol{{tangent}}\:\boldsymbol{{at}}\:\boldsymbol{{x}}=\mathrm{0}\:\boldsymbol{{so}}\:\boldsymbol{{there}}\:\boldsymbol{{is}}\:\boldsymbol{{no}}\:\boldsymbol{{differentiable}}\:\boldsymbol{{at}}\:\boldsymbol{{x}}=\mathrm{0} \\$$
Commented by mr W last updated on 05/Mar/21
$${can}\:{you}\:{show}\:{us}\:{how}\:{your}\:{graph}\:{for} \\$$$${sin}\:{x}\:{looks}\:{like}? \\$$$${btw}:\:{please}\:{don}'{t}\:{write}\:{all}\:{things} \\$$$${in}\:{only}\:{one}\:{single}\:{line}!\:{thanks}! \\$$