Check Full Chapter Explained - Continuity and Differentiability - Application of Derivatives (AOD) Class 12


Last updated at Dec. 8, 2016 by Teachoo
Check Full Chapter Explained - Continuity and Differentiability - Application of Derivatives (AOD) Class 12
Transcript
Ex 6.3,6 Find the slope of the normal to the curve ð¥=1âð sinâ¡ð , ð¦ =ð cosï·®2ï·¯ ð at ð= ðï·®2ï·¯ Slope of tangent is ðð¦ï·®ðð¥ï·¯ ðð¦ï·®ðð¥ï·¯= ðð¦ï·®ðð﷯﷮ ðð¥ï·®ðð﷯﷯ Now, ðð¦ï·®ðð¥ï·¯= ðð¦ï·®ðð﷯﷮ ððï·®ðð﷯﷯ ðð¦ï·®ðð¥ï·¯= â 2ð sinï·®ð cosï·®ð﷯﷯﷮â ð cosï·®ð﷯﷯ ðð¦ï·®ðð¥ï·¯= 2ð sinï·®ð﷯﷮ðï·¯ We need to find Slope of tangent at ð= ðï·®2ï·¯ Putting ð= ðï·®2ï·¯ ðð¦ï·®ðð¥ï·¯ï·¯ï·®ð = ðï·®2﷯﷯= 2ðï·®ðï·¯ ð ðð ðï·®2﷯﷯ = 2ðï·®ðï·¯ 1ï·¯ We know that Tangent is Perpendicular to Normal Hence Slope of tangent à Slope of Normal =â1 Slope of Normal = â 1ï·®ððððð ðð ð¡ðððððð¡ ï·¯ Slope of Normal = â 1ï·® ðð¦ï·®ðð¥ï·¯ï·¯ Slope of Normal =â1 à ðï·®2ðï·¯ Slope of Normal = âðï·®2ðï·¯ Hence Slope of Normal at is âðï·®ððï·¯
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