Targate

Question

How to solve this?

Answer 1

$\lim_{x\rightarrow \infty }(\frac{x+a}{x+b})^{x+c} = e^{a-b}$

so, here

$\lim_{x\rightarrow \infty }(\frac{x+5}{x+2})^{x+3} = e^{5-2} = e^3$

Comments

@Lokesh, Cnt it be done like this?

F = Numerator / Denominator  = $\frac{x+a}{x+b}$ = $\frac{1+\frac{a}{x}}{1+\frac{b}{x}}$

Now, as x $\rightarrow$ infinitity,   F $\rightarrow$ 1 ,right?

Now, 1^{any power}  = 1

So, shouldnt the answer be 1?

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acrdng to you ans should be $1^\infty$ but this is an indeterminate form in the limits for which further evaluation is needed

see ref: https://en.wikipedia.org/wiki/Indeterminate_form

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ok, :)  Thanks

Answer 2

srry for the pic quality