The correct option is A e We have,lim_x→∞(x+2/x+1)^x+1 At x=∞,the value of the given expression is 1^∞ form lim_x→∞(1+x+1/x+1)^x+1 lim_x→∞(1+1/x+1)^x+1 ...

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Second Fundamental Theorem of Calculus

lim x →∞x+2/x...

Question

$lim x \to \infty {(\frac{x + 2}{x + 1})}^{x + 1}$ is

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Solution

The correct option is A
e

We have, $lim x \to \infty {(\frac{x + 2}{x + 1})}^{x + 1}$

At $x = \infty, t h e v a l u e o f t h e g i v e n e x p r e s s i o n i s 1^{\infty}$ form

$lim x \to \infty {(\frac{1 + x + 1}{x + 1})}^{x + 1}$

$lim x \to \infty {(1 + \frac{1}{x + 1})}^{x + 1}$

We can compare the given limit with

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

So, $lim x \to \infty {(1 + \frac{1}{x + 1})}^{x + 1}$

$= e$

Option A is correct

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limx→∞(x+2x+1)x+1 is

The correct option is A e We have,limx→∞(x+2x+1)x+1 At x=∞,the value of the given expression is 1∞ form limx→∞(1+x+1x+1)x+1 limx→∞(1+1x+1)x+1 We can compare the given limit with limx→∞(1+1x+1)x=e So,limx→∞(1+1x+1)x+1 =e Option A is correct

$lim x \to \infty {(\frac{x + 2}{x + 1})}^{x + 1}$ is