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AP EAMCET201822 Apr 2018Morning ShiftMathematicsApplication of DerivativesActual

The approximate value of 31^ is ( . Take .1^ =0.0174 )

Options

  1. A0.7521
  2. B0.866
  3. C0.7146
  4. D0.8573

Correct answer

D. 0.8573

Step-by-step solution

Let y= (x), x=30^ and x+ x=31^ Let us find (y)_ x= 6 = ( 6 )= 3 2 Then, x=1^ =0.0174 radian. Consider the given function, y=f(x)= (x) Differentiating w.r.t. x , aligned d y d x & =- (x) ( d y d x )_ x= 6 & =- 6 ( d y d x )_x= 6 & =- 1 2 aligned Let y be the change in y due to the change x in x . aligned y & = d y d x x & = (- 1 2 ) 0.0174 & =(-0.5) 0.0174=-0.0087 f (36^ ) & =y+ y = & 3 2 -0.0087 & = 1.732 2 -0.0087 & =0.8660-0.0087 & =0.8573 aligned

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