Q. 205.0( 1 Vote )

Evaluate the foll

Answer :


Formula used:



where,



Here, a = 1 and b = 4


Therefore,




Let,



Here, f(x) = 3x2 + 2x and a = 1



Now, by putting x = 1 in f(x) we get,


f(1) = 3(1)2 + 2(1) = 3 + 2 = 5


f(1 + h)


= 3(1 + h)2 + 2(1 + h)


= 3{h2 + 12 + 2(h)(1)} + 2 + 2h


= 3h2 + 3 + 6h + 2 + 2h


= 3h2 + 8h + 5


Similarly, f(1 + 2h)


= 3(1 + 2h)2 + 2(1 + 2h)


= 3{(2h)2 + 12 + 2(2h)(1)} + 2 + 4h


= 3(2h)2 + 3 + 6(2h) + 2 + 2(2h)


= 3(2h)2 + 8(2h) + 5


{ (x + y)2 = x2 + y2 + 2xy}




Since 5 is repeating n times in series




Now take 3h2 and 8h common in remaining series





Put,



Since,















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