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  • Confused! kindly explain, - Limit , continuity and differentiability - JEE Main-11

Right hand derivative of f(x)= \sin|x| + |x| at x=0 equals

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 As we have learned

Right Hand Derivatives -

Right hand derivative of  f(x) at  x=x_{\circ }  is given by  

f'(x_{\circ })=\lim_{h\rightarrow 0}\:\:\frac{f(x_{\circ }+h)-f(x_{\circ })}{(x_{\circ }+h)-(x_{\circ })}

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RHD = \lim_{h\rightarrow 0^{+}}\frac{f(0-h)-f(0)}{(0-h)-0}=\lim_{h\rightarrow 0^{+}}\frac{\sin |h|+|h|-0}{h }

=\lim_{h\rightarrow 0^{+}}\frac{\sin h+h}{h }=\lim_{h\rightarrow 0^{+}}\frac{\sin h}{h + \lim_{h\rightarrow 0^{+}}}\frac{h}{h}

=1+1=2 

 

 

 

 

 


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