MHT CET202014 Oct 2020Evening ShiftMathematicsApplication of DerivativesActual

The approximate value of ₁₀ 99 is ( . Given ₁₀ e =0.4343 )

Options

A1.9657
B1.9857
C1.1 .9957
D1.9757

Correct answer

C. 1.1 .9957

Step-by-step solution

Let f(x)= ₁₀ x= _ e x _ e 10 f^ (x)= 1 x 10 Let a =100, ~h =-1 f(a)= ₁₀ 100 = ₁₀ 10²=2f^ (a)= 1 100 _ e 10 = 1 100 ₁₀ e= 1 100 0.4343 We know that aligned f(a-h) & f(a)+h f^ (a) & 2+(-1) 1 100 (0.4343)=2-0.004343=1.995657 & 1.9957 aligned

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