Evaluate :
$$\left(1+\sqrt{x^{2}-1}\right)^{6}+\left(x-\sqrt{x^{2}-1}\right)^{6}$$

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{lim}_{x \to 4} \frac{x^{2} - 16}{\sqrt{x^{2} + 9} - 5}

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Evaluate the following:
(i)

{(\sqrt{x + 1} + \sqrt{x - 1})}^{6} + {(\sqrt{x + 1} - \sqrt{x - 1})}^{6}

(ii)

{(x + \sqrt{x^{2} - 1})}^{6} + {(x - \sqrt{x^{2} - 1})}^{6}

(iii)

{(1 + 2 \sqrt{x})}^{5} + {(1 - 2 \sqrt{x})}^{5}

(iv)

{(\sqrt{2} + 1)}^{6} + {(\sqrt{2} - 1)}^{6}

(v)

{(3 + \sqrt{2})}^{5} - {(3 - \sqrt{2})}^{5}

(vi)

{(2 + \sqrt{3})}^{7} + {(2 - \sqrt{3})}^{7}

(vii)

{(\sqrt{3} + 1)}^{5} - {(\sqrt{3} - 1)}^{5}

(viii)

{(0.99)}^{5} + {(1.01)}^{5}

(ix)

{(\sqrt{3} + \sqrt{2})}^{6} - {(\sqrt{3} - \sqrt{2})}^{6}

(x)

{\{a^{2} + \sqrt{a^{2} - 1}\}}^{4} + {\{a^{2} - \sqrt{a^{2} - 1}\}}^{4}

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Evaluate the limit:

lim x \to 4 \frac{x^{3} - 64}{x^{2} - 16}

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Evaluate:

lim x \to 4 (\frac{x^{3} - 64}{x^{2} - 16})

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Evaluate the following:

$(i) (\sqrt{x + 1} + \sqrt{x - 1})^{6} + (\sqrt{x + 1} - \sqrt{x - 1})^{6}$

$(i i) (x + \sqrt{x^{2} - 1})^{6} + (x - \sqrt{x^{2} - 1})^{6}$

$(i i i) (1 + 2 \sqrt{x})^{5} + (1 - 2 \sqrt{x})^{5}$

$(i v) (\sqrt{2} + 1)^{6} + (\sqrt{2} - 1)^{6}$

$(v) (3 + \sqrt{2})^{5} - (3 - \sqrt{2})^{5}$

$(v i) (2 + \sqrt{3})^{7} + (2 - \sqrt{3})^{7}$

$(v i i) (\sqrt{3} + 1)^{5} - (\sqrt{3} - 1)^{5}$

$(v i i i) (0.99)^{5} + (1.01)^{5}$

$(i x) (\sqrt{3} + \sqrt{2})^{6} - (\sqrt{3} - \sqrt{2})^{6}$

$(x) {a^{2} + \sqrt{a^{2} - 1}}^{4} + {a^{2} - \sqrt{a^{2} - 1}}^{4}$

View Solution

Evaluate :$$\left(1+\sqrt{x^{2}-1}\right)^{6}+\left(x-\sqrt{x^{2}-1}\right)^{6}$$