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MHT CET20239 May 2023Morning ShiftMathematicsApplication of DerivativesActual

The approximate value of ₁₀ 998 is (given that ₁₀ e =0.4343 )

Options

  1. A3.0008686
  2. B1.9991314
  3. C2.0008686
  4. D2.9991314

Correct answer

D. 2.9991314

Step-by-step solution

Let aligned f (x)= ₁₀ x= _ e x _ e 10 & = ( ₁₀ e ) ( _ e x ) & =0.4343 ( _ e x ) aligned On differentiating w.r.t. x , we get aligned f ^ (x) & = 0.4343 x Let x & =998 & =1000-2= a + h a = & 1000, ~h =-2 f ( a ) & = f (1000) & = ₁₀(1000) & =3 ₁₀ 10 f ( a ) & =3 aligned aligned & Also, f ^ ( a )= f ^ (1000)= 0.4343 1000 =0.0004343 & f ( a + h ) f ( a )+ hf ^ ( a ) & ₁₀(998) 3-2(0.0004343) & aligned

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