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Grade 12Differential Calculus

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milind

12 Years agoGrade 12

1 Answer

Jitender Singh

12 Years ago

Hello student,
Please find answer to your question
$f(x) = x^{n} + 4$
$f'(x) = nx^{n-1}$
$L = 5 + n + \frac{n(n-1)}{2!}+..........+\frac{n!}{n!}$
$L = 4 + 1 + n + \frac{n(n-1)}{2!}+..........+\frac{n!}{n!}$
$L = 4 + (1 + n + \frac{n(n-1)}{2!}+..........+\frac{n!}{n!})$
By binomiam 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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