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Differential Calculus> Help please image attached...

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Help please image attached

milind , 11 Years ago

Grade 12

1 Answers

Jitender Singh

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
$2^{n} = (1+1)^{n} = 1 + n + \frac{n(n-1)}{2!}+...................+\frac{n!}{n!}$
$L = 2^{n} + 4$

Last Activity: 11 Years ago

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