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Question Number 134519 by sachin1221 last updated on 04/Mar/21

why sinx is not differentiable at x=nπ

$${why}\:{sinx}\:{is}\:{not}\:{differentiable}\:{at}\:{x}={n}\pi \\ $$

Commented by JDamian last updated on 04/Mar/21

seriously?

Answered by physicstutes last updated on 04/Mar/21

lim_(x→0) (((sinx−0)/(x−0))) = lim_(x→0) ((sin x)/x) = 1 sin x is also continuous and so it is differentiable at x = 0. what do you mean by your question?

$$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\left(\frac{\mathrm{sin}{x}−\mathrm{0}}{{x}−\mathrm{0}}\right)\:=\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{sin}\:{x}}{{x}}\:=\:\mathrm{1} \\ $$$$\mathrm{sin}\:{x}\:\mathrm{is}\:\mathrm{also}\:\mathrm{continuous}\:\mathrm{and}\:\mathrm{so}\:\mathrm{it}\:\mathrm{is}\:\mathrm{differentiable}\:\mathrm{at}\: \\ $$$$\:{x}\:=\:\mathrm{0}.\:\mathrm{what}\:\mathrm{do}\:\mathrm{you}\:\mathrm{mean}\:\mathrm{by}\:\mathrm{your}\:\mathrm{question}? \\ $$

Commented by sachin1221 last updated on 04/Mar/21

lim_(x→0) (((sinx−0)/(x−0))) = lim_(x→0) ((sin x)/x) = 1 sin x is also continuous and so it is differentiable at x = 0. what do you mean by your question? but when u see graphical method at x=0 u will get infinite tangent at x=0 so there is no differentiable at x=0

$$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\left(\frac{\mathrm{sin}{x}−\mathrm{0}}{{x}−\mathrm{0}}\right)\:=\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{sin}\:{x}}{{x}}\:=\:\mathrm{1} \\ $$$$\mathrm{sin}\:{x}\:\mathrm{is}\:\mathrm{also}\:\mathrm{continuous}\:\mathrm{and}\:\mathrm{so}\:\mathrm{it}\:\mathrm{is}\:\mathrm{differentiable}\:\mathrm{at}\: \\ $$$$\:{x}\:=\:\mathrm{0}.\:\mathrm{what}\:\mathrm{do}\:\mathrm{you}\:\mathrm{mean}\:\mathrm{by}\:\mathrm{your}\:\mathrm{question}? \\ $$$${but}\:{when}\:\boldsymbol{{u}}\:\boldsymbol{{see}}\:\boldsymbol{{graphical}}\:\boldsymbol{{method}}\:\boldsymbol{{at}}\:\boldsymbol{{x}}=\mathrm{0}\:\boldsymbol{{u}}\:\boldsymbol{{will}}\:\boldsymbol{{get}}\:\boldsymbol{{infinite}}\:\boldsymbol{{tangent}}\:\boldsymbol{{at}}\:\boldsymbol{{x}}=\mathrm{0}\:\boldsymbol{{so}}\:\boldsymbol{{there}}\:\boldsymbol{{is}}\:\boldsymbol{{no}}\:\boldsymbol{{differentiable}}\:\boldsymbol{{at}}\:\boldsymbol{{x}}=\mathrm{0} \\ $$

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!

$${can}\:{you}\:{show}\:{us}\:{how}\:{your}\:{graph}\:{for} \\ $$$${sin}\:{x}\:{looks}\:{like}? \\ $$$${btw}:\:{please}\:{don}'{t}\:{write}\:{all}\:{things} \\ $$$${in}\:{only}\:{one}\:{single}\:{line}!\:{thanks}! \\ $$

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