Q. 325.0( 1 Vote )

Evaluate the foll

Answer :


Formula used:



where,



Here, a = 1 and b = 3


Therefore,




Let,



Here, f(x) = 2x2 + 5x and a = 1



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


f(1) = 2(1)2 + 5(1) = 2 + 5 = 7


f(1 + h)


= 2(1 + h)2 + 5(1 + h)


= 2{h2 + 12 + 2(h)(1)} + 5 + 5h


= 2h2 + 4h + 2 + 5 + 5h


= 2h2 + 9h + 7


Similarly, f(1 + 2h)


= 2(1 + 2h)2 + 5(1 + 2h)


= 2{(2h)2 + 12 + 2(2h)(1)} + 5 + 10h


= 2(2h)2 + 2 + 8h + 5 + 10h


= 2(2h)2 + 18h + 7


= 2(2h)2 + 9(2h) + 7


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




In this series, 7 is getting added n times



Now take 2h2 and 9h common in remaining series





Put,



Since,
















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