The correct option is C e^4 lim _ x→∞ #160; ( x ^ 2 +5x+3 x ^ 2 +x+2 #160; ) #160; ^ x #160; 1 ^∞ form = e ^lim _ x→∞ #160; ...

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Integration of Irrational Algebraic Fractions - 1

x→∞limx2+5x+3...

Question

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

e^{4}

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e^{3}

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e^{2}

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2^{4}

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Solution

The correct option is C $e^{4}$
$lim x \to \infty {(\frac{x^{2} + 5 x + 3}{x^{2} + x + 2})}^{x} - 1^{\infty}$ form

$= e^{lim x \to \infty x (\frac{x^{2} + 5 x + 3}{x^{2} + x + 2} - 1)}$

$= e^{lim x \to \infty x (\frac{4 x + 1}{x^{2} + x + 2})}$

$= e^{lim x \to \infty \frac{x^{2}}{x^{2}} ⎛ ⎜ ⎜ ⎜ ⎝ \frac{4 + \frac{1}{x}}{1 + \frac{1}{x} + \frac{2}{x^{2}}} ⎞ ⎟ ⎟ ⎟ ⎠}$ , $[x \to \infty, \frac{1}{x} \to 0]$
$= e^{\frac{4 + 0}{1 + 0 + 0}} = e^{4}$

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Similar questions

Q. Evaluate

l i m x \to \infty {(\frac{x^{2} + 5 x + 3}{x^{2} + x + 2})}^{x} = e^{a}

. Find

a

Q. Assertion

(A) : lim x \to \infty {(\frac{x^{2} + 5 x + 3}{x^{2} + x + 2})}^{x} = e^{4}

Reason

(R) : lim x \to \infty {(1 + x)}^{\frac{1}{x}} = e

Q. Evaluate :

\int_{0}^{1} \frac{e^{5 l n x} - e^{4 l n x}}{e^{3 l n x} - e^{2 l n x}} d x

Q. Assertion(A):

lim x \to \infty {(\frac{x^{2} + 5 x + 3}{x^{2} + x + 2})}^{x} = e^{4}

Reason(R):

lim x \to \infty (1 + x)^{1 / x} = e

The figure gives the electric potential $V$ as a function of distance through five regions on $x -$ axis. Which of the following is true for the electric field $E$ in these regions?

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limx→∞(x2+5x+3x2+x+2)x=

The correct option is C e4limx→∞(x2+5x+3x2+x+2)x−1∞form=elimx→∞x(x2+5x+3x2+x+2−1)=elimx→∞x(4x+1x2+x+2)=elimx→∞x2x2⎛⎜ ⎜ ⎜⎝4+1x1+1x+2x2⎞⎟ ⎟ ⎟⎠ ,[x→∞,1x→0]=e4+01+0+0=e4

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