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Expansion of (x+a)(x+b)

if x+1/x=2 ...

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if x+1/x=2 then find the value of x^{100}+1/x^{100} ,find attached solutio

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x > 0

, then find greatest value of the expression

\frac{x^{100}}{1 + x + x^{2} + x^{3} + . . . . + x^{200}}

f (x) = 1 + x + x^{2} + . . . . . + x^{100}

f^{'} (1)

(x^{100} + 2 x^{99} + K)

is exactly divisible by

(x + 1)

, find the value of 'K'

x^{50} + \frac{1}{x^{50}} = 2

x^{100} + \frac{1}{x^{100}} =

Q. (i) Evaluate

{lim}_{x \to \frac{π}{6}} \frac{\sqrt{3} s i n x - c o s x}{x - \frac{π}{6}}

f (x) = 1 + x + \frac{x^{2}}{2} + . . . + \frac{x^{100}}{100},

then find the value of f'(1).

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