The approximate value of ₁₀ 1002 is (Given ₁₀ e =0.4343 )

Step-by-step solution

aligned & Let f (x)= _e x & f ^ (x)= 1 x & Here, a=1000, ~h =2 & f ( a + h ) f ( a )+ hf ^ ( a ) & f(1000)+2 f^ (1000) & _ e 10^3+2 1 1000 & 3(0.4343)+0.002 & 1.3029+0.002 & 1.3049 & _ e 1002 1.3049 & Now, ₁₀ 1002 _ e 1002 _ e 10 & 1.3049 0.4343 3.0009 aligned