Let P(x)=a1x+a2x2+a3x3+......+a100x100, where a1=1 and ai∈R∀i=2,3,4,......100, then limx→01+P(x)100−1x has the value equal to:

l=limx→0(1+P(x))1/n−1xa 9Using binomial expansion)=limx→0(1+1nP(x)+.......)−1x=limx→01n[a1x+a2x2+a3x3+......x]=a1n

Let P(x)=a1x+a2x2+a3x3+......+a100x100, where a1=1 and ai∈R∀i=2,3,4,......100, then limx→01+P(x)100−1x has the value equal to:

l=limx→0(1+P(x))1/n−1xa 9Using binomial expansion)=limx→0(1+1nP(x)+.......)−1x=limx→01n[a1x+a2x2+a3x3+......x]=a1n

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Let $P (x) = a_{1} x + a_{2} x^{2} + a_{3} x^{3} + ...... + a_{100} x^{100}$ , where $a_{1} = 1$ and $a_{i} \in R \forall i = 2, 3, 4, ......100$ , then $\lim_{x \to 0} \frac{\sqrt[100]{1 + P (x)} - 1}{x}$ has the value equal to:

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$l = \lim_{x \to 0} \frac{{(1 + P (x))}^{1 / n} - 1}{x} a$ 9Using binomial expansion)

$= \lim_{x \to 0} \frac{(1 + \frac{1}{n} P (x) + .......) - 1}{x} = \lim_{x \to 0} \frac{1}{n} [\frac{a_{1} x + a_{2} x^{2} + a_{3} x^{3} + ......}{x}] = \frac{a_{1}}{n}$

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Let P(x)=a1x+a2x2+a3x3+......+a100x100, where a1=1 and ai∈R∀i=2,3,4,......100, then limx→01+P(x)100−1x has the value equal to:

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Let $P (x) = a_{1} x + a_{2} x^{2} + a_{3} x^{3} + ...... + a_{100} x^{100}$ , where $a_{1} = 1$ and $a_{i} \in R \forall i = 2, 3, 4, ......100$ , then $\lim_{x \to 0} \frac{\sqrt[100]{1 + P (x)} - 1}{x}$ has the value equal to: