Q. 10

# Evaluate the foll

Formula used:

where,

Here, a = 2 and b = 3

Therefore,

Let,

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

Now, by putting x = 2 in f(x) we get,

f(2) = 2(22) + 1 = 2(4) + 1 = 8 + 1 = 9

f(1 + h)

= 2(2 + h)2 + 1

= 2{h2 + 22 + 2(h)(2)} + 1

= 2(h)2 + 8 + 2(4h) + 1

= 2(h)2 + 9 + 8(h)

Similarly, f(2 + 2h)

= 2(2 + 2h)2 + 1

= 2{2(2h)2 + 22 + 2(2h)(2)} + 1

= 2(2h)2 + 8 + 8(2h) + 1

= 2(2h)2 + 9 + 8(2h)

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

In this series, 9 is getting added n times

Now take 2h2 and 4h common in remaining series

Put,

Since,

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