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`lim_(x to pi//4)(sin x- cos x)/(x- pi//4)` का मान ज्ञात कीजिये।

Answer» `underset(x to pi//4)lim(sinx-cos x)/(x-pi//4)`
माना `x=pi//4+h,` यदि `x=pi//4 impliesh=0`
`therefore x to pi//4 impliesh to 0`
`thereforeunderset(xto pi//4)lim(sin x-cos x)/(x- pi//4)=underset(xto0)lim(sin (pi//4+h)-cos (pi//4+h))/((pi)/(4)+h-(pi)/(h))`
`=underset(hto0)lim((sinpi//4cos h+cos pi//4sin h)-(cos pi//4cos h-sin pi//4sin h))/(h)`
`=underset(xto0)lim (1)/(sqrt2)((cos h+sin h-cos h+sin h))/(h)(cos pi//4=sin pi//4+(1)/(sqrt2))`
`=(1)/(sqrt2)underset(hto0)lim (2 sin h)/(h)=sqrt2underset(hto0)lim(sin h)/(h)`
`=sqrt2xx1=sqrt2" "(becauseunderset(h to 0)lim(sin h)/(h)=1)`


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