Limx - 1xm - 1xn - 1 is

The correct option is A mn lim_x→ 1(x^m 1x^n 1) apply l hospital rule lim_x→ 1(mx^mnx^n) Now,put the value of x=1 = gt;m× x^mn× x^n ...

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Differentiation under Integral Sign

limx → 1xm - ...

Question

$lim x \to 1 \frac{x^{m} - 1}{x^{n} - 1} i s$

1

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\frac{m}{n}

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- \frac{m}{n}

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\frac{m^{2}}{n^{2}}

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Solution

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lim x \to 1 \frac{x^{m} - 1}{x^{n} - 1}

lim x \to 1 \frac{x^{m} - 1}{x^{n} - 1} .

m = \sqrt[3]{15}

n = \sqrt[3]{14}

m - n - \frac{1}{m^{2} + m n + n^{2}}

m^{2} + {m^{'}}^{2} + 2 m m^{'} cos x = 1

n^{2} + {n^{'}}^{2} + 2 n n^{'} cos x = 1

m n + m^{'} n^{'} + (m n^{'} + m^{'} n) cos x = 0

m^{2} + n^{2} = c o {sec}^{2} x

{m^{'}}^{2} + {n^{'}}^{2} = c o {sec}^{2} x

If the coefficient of $m^{t h}$ , $(m + 1)^{t h}$ and $(m + 2)^{t h}$ terms in the expansion of $(1 + x)^{n}$ are in A.P., then:

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