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Application Of Derivatives

Question
CBSEENMA12035105
Wired Faculty App

Find the equation of the tangent to the curve
straight y space equals space fraction numerator 1 plus sinx over denominator cosx end fraction space at space straight x space equals space straight pi over 4.

Solution

The equation of curve is
                    straight y space equals space fraction numerator 1 plus sinx over denominator cosx end fraction space equals space 1 over cosx plus sinx over cosx space equals space secx plus tanx
At space straight x space equals space straight pi over 4 comma space space space straight y space equals sec straight pi over 4 plus tan straight pi over 4 space equals space square root of 2 plus 1 therefore space space space space points space is space open parentheses straight pi over 4 comma space space square root of 2 plus 1 close parentheses space space space space space space space space space space space space space space dy over dx space equals space sec space straight x space tanx space plus sec squared straight x space equals space secx left parenthesis tanx space plus sec space straight x right parenthesis At space space space straight x space equals straight pi over 4 comma space space dy over dx space equals space sec straight pi over 4 open parentheses tan space straight pi over 4 space plus space sec space straight pi over 4 close parentheses space equals space square root of 2 left parenthesis 1 plus square root of 2 right parenthesis therefore space space space space equation space of space tangent space at space open parentheses straight pi over 4 comma space space space square root of 2 plus 1 close parentheses space space space is space space space space space space space space space space space space space space space straight y minus left parenthesis square root of 2 plus 1 right parenthesis space equals space square root of 2 left parenthesis 1 plus square root of 2 right parenthesis space open parentheses straight x minus straight pi over 4 close parentheses or space space space space space space space space space space straight y minus left parenthesis square root of 2 plus 1 right parenthesis space equals space square root of 2 left parenthesis 1 plus square root of 2 right parenthesis straight x minus fraction numerator square root of 2 left parenthesis 1 plus square root of 2 right parenthesis straight pi over denominator 4 end fraction space or space space space space space space space space space space 4 square root of 2 left parenthesis 1 plus square root of 2 right parenthesis straight x minus 4 straight y plus 4 left parenthesis square root of 2 plus 1 right parenthesis minus square root of 2 left parenthesis 1 plus square root of 2 right parenthesis space straight pi space equals space 0 space

Some More Questions From Application of Derivatives Chapter

The radius of a circle is increasing uniformly at the rate of 4 cm per second Find the rate at which the area of the circle is increasing when the radius is 8 cm.

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