I Find the derivative of -x-1x-2-x-3x-4-sin x-1-tan xii Evaluate lim X - 01- x 6-1-1- x 2-1

(i) 1/2√((x 1)(x 2)/(x 3)(x 4)) [ 1/x 1+1/x 2 1/x 3 1/x 4 ]+cos x + sin x sin x sec^2 x/(1 + tan x)^2 (ii) 3 ...

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i Find the de...

Question

(i) Find the derivative of $\sqrt{\frac{(x - 1) (x - 2)}{(x - 3) (x - 4)}}$ + $\frac{s i n x}{1 + t a n x}$

(ii) Evaluate ${lim}_{x \to 0} \frac{(1 + x)^{6} - 1}{(1 + x)^{2} - 1}$

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{lim}_{x \to 0} \frac{(1 + x)^{6} - 1}{(1 + x)^{2} - 1}

(i) Evaluate ${lim}_{x \to 1} \frac{x + x^{2} + x^{3} + . . . + x^{n} - n}{x - 1}$

(ii) Find the derivative $\sqrt{sin x}$ from first principle.

Evaluate $l i m x \to 0 \frac{(1 + x)^{6} - 1}{(1 + x)^{5} - 1}$

lim x \to 0 \frac{{(1 + x)}^{6} - 1}{{(1 + x)}^{5} - 1}

${lim}_{x \to 0} \frac{(1 + x)^{6} - 1}{(1 + x)^{2} - 1}$

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