Evaluate lim x - 2x5-32-x3-8

X→2lim ( x^5 32/x^3 8 ) = x→2lim ( x^5 2^5/x^3 2^3 ) =x→ 2lim{ ( x^5 2^5/x 2 ) + ( x^3 2^3/x 2 )} =x→ 2lim ( x^5 2^5/x 2 ) + x → 2lim ( x^3 2^3/x 2 ) =[(5× 2^4 ...

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Byju's Answer

Standard XII

Mathematics

Theorems for Continuity

Evaluate lim ...

Question

Evaluate $l i m x \to 2 (\frac{x^{5} - 32}{x^{3} - 8})$

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Solution

$l i m x \to 2 (\frac{x^{5} - 32}{x^{3} - 8})$ $= l i m x \to 2 (\frac{x^{5} - 2^{5}}{x^{3} - 2^{3}})$

$= l i m x \to 2 {(\frac{x^{5} - 2^{5}}{x - 2}) + (\frac{x^{3} - 2^{3}}{x - 2})}$

$= l i m x \to 2 (\frac{x^{5} - 2^{5}}{x - 2}) + l i m x \to 2 (\frac{x^{3} - 2^{3}}{x - 2})$

$= [(5 \times 2^{4}) + (3 \times 2^{2})] [∵ l i m x \to a (\frac{x^{n} - a^{n}}{x - a}) = n a^{n - 1}]$

$= (\frac{80}{12}) = \frac{20}{3}$

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Q. Evaluate

lim x \to_{2} \frac{x^{5} + 32}{x^{3} + 8}

lim x \to - 2 \frac{x^{5} + 32}{x^{3} + 8}

{lim}_{x \to 2} \frac{x^{5} - 32}{x^{3} - 8} =

{lim}_{x \to 2} \frac{x^{5} - 32}{x^{3} - 8}

lim x \to 2 \frac{x^{5} \sqrt{x} - 32 \sqrt{2}}{x^{3} \sqrt{x} - 8 \sqrt{2}}

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Evaluate limx→2(x5−32x3−8)

limx→2(x5−32x3−8) =limx→2(x5−25x3−23) =limx→2{(x5−25x−2)+(x3−23x−2)} =limx→2(x5−25x−2)+limx→2(x3−23x−2) =[(5×24)+(3×22)] [∵limx→a(xn−anx−a)=nan−1] =(8012)=203

Evaluate $l i m x \to 2 (\frac{x^{5} - 32}{x^{3} - 8})$