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Grade:12

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Jitender Singh IIT Delhi
askIITians Faculty 158 Points
9 years ago
Hello student,
Please find answer to your question
f(x) = x^{n} + 4
f'(x) = nx^{n-1}
L = f(1) + \frac{f'(1)}{1!}+\frac{f''(1)}{2!}+.............+\frac{f^{n}(1)}{n!}
L = 4+1 + \frac{n}{1!}+\frac{n(n-1)}{2!}+.............+\frac{n!}{n!}
L = 4+(1 + \frac{n}{1!}+\frac{n(n-1)}{2!}+.............+\frac{n!}{n!})
By using binomial theorm, we have
2^{n} = (1+1)^{n} = 1 + n + \frac{n(n-1)}{2!}+...................+\frac{n!}{n!}
L = 2^{n} + 4

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