X-lim - 3x-2-2x-1-x-2-x-2 -6x-1-3x-2is equal to3-9-1-4-

The correct option is B 9 x→∞lim ( 3x^2+2x+1/x^2+x+2 )^6x+1/3x+2 x→∞lim ( 3+2/x+1/x^2/1+1/x+2/x^2 )^6+1/3/3+2/x= ( 3/1 )^6/3=9 ...

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Byju's Answer

Standard XII

Mathematics

Indeterminate Forms

x→∞lim ( 3x^2...

Question

$l i m x \to \infty {(\frac{3 x^{2} + 2 x + 1}{x^{2} + x + 2})}^{\frac{6 x + 1}{3 x + 2}} is equal to$

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Solution

The correct option is B
9

$l i m x \to \infty {(\frac{3 x^{2} + 2 x + 1}{x^{2} + x + 2})}^{\frac{6 x + 1}{3 x + 2}} l i m x \to \infty {(\frac{3 + \frac{2}{x} + \frac{1}{x^{2}}}{1 + \frac{1}{x} + \frac{2}{x^{2}}})}^{\frac{6 + \frac{1}{3}}{3 + \frac{2}{x}}} = {(\frac{3}{1})}^{6 / 3} = 9$

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Similar questions

Q. Which of the following are quadratic equations?

(i) x² + 6x − 4 = 0
(ii)

\sqrt{3} x^{2} - 2 x + \frac{1}{2} = 0

(iii)

x^{2} + \frac{1}{x^{2}} = 5

(iv)

x - \frac{3}{x} = x^{2}

(v)

2 x^{2} - \sqrt{3 x} + 9 = 0

(vi)

x^{2} - 2 x - \sqrt{x} - 5 = 0

(vii) 3x² − 5x + 9 = x² − 7x + 3
(viii)

x + \frac{1}{x} = 1

(ix) x² − 3x = 0
(x)

{(x + \frac{1}{x})}^{2} = 3 (x + \frac{1}{x}) + 4

(xi) (2x + 1) (3x + 2) = 6(x − 1) (x − 2)
(xii)

x + \frac{1}{x} = x^{2}, x \neq 0

(xiii) 16x² − 3 = (2x + 5) (5x − 3)
(xiv) (x + 2)³ = x³ − 4
(xv) x(x + 1) + 8 = (x + 2) (x − 2)

Check whether the following are quadratic equations :
(i) ${(x + 1)}^{2} = 2 (x - 3)$
(ii) $x^{2} - 2 x = (- 2) (3 - x)$
(iii) $(x - 2) (x + 1) = (x - 1) (x + 3)$
(iv) $(x - 3) (2 x + 1) = x (x + 5)$
(v) $(2 x - 1) (x - 3) = (x + 5) (x - 1)$
(vi) $x^{2} + 3 x + 1 = {(x - 2)}^{2}$
(vii) ${(x + 2)}^{3} = 2 x (x^{2} - 1)$
(viii) $x^{3} - 4 x^{2} - x + 1 = {(x - 2)}^{3}$

$l i m x \to \infty {(\frac{3 x^{2} + 2 x + 1}{x^{2} + x + 2})}^{\frac{6 x + 1}{3 x + 2}} is equal to$

lim x \to \infty {(\frac{3 x^{2} + 2 x + 1}{x^{2} + x + 2})}^{\frac{6 x + 1}{3 x + 2}}

is equal to

$l i m x \to \infty {(\frac{3 x^{2} + 2 x + 1}{x^{2} + x + 2})}^{\frac{6 x + 1}{3 x + 2}} is equal to$

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limx→∞(3x2+2x+1x2+x+2)6x+13x+2is equal to

The correct option is B 9 limx→∞(3x2+2x+1x2+x+2)6x+13x+2limx→∞(3+2x+1x21+1x+2x2)6+133+2x=(31)6/3=9

$l i m x \to \infty {(\frac{3 x^{2} + 2 x + 1}{x^{2} + x + 2})}^{\frac{6 x + 1}{3 x + 2}} is equal to$

The correct option is B
9

$l i m x \to \infty {(\frac{3 x^{2} + 2 x + 1}{x^{2} + x + 2})}^{\frac{6 x + 1}{3 x + 2}} l i m x \to \infty {(\frac{3 + \frac{2}{x} + \frac{1}{x^{2}}}{1 + \frac{1}{x} + \frac{2}{x^{2}}})}^{\frac{6 + \frac{1}{3}}{3 + \frac{2}{x}}} = {(\frac{3}{1})}^{6 / 3} = 9$