limit

evaluate the limit:

\lim_{x\rightarrow \propto } \frac{x^{2}(1+sin^{2}x)}{(x+sinx)^{2}}

4 Answers

21
Shubhodip ·

using x→∞ lim (sin x)/x = 0

the answer comes to be 1

1
pritishmasti ............... ·

i am not getting any answer

\lim_{x\rightarrow \propto } \frac{x^{2}(1+sin^{2}x)}{(x+sinx)^{2}} \Rightarrow lim_{x\rightarrow \propto } \frac{x^{2}(1+sin^{2}x)}{x^{2}(1+\frac{sinx}{x})^{2}} \Rightarrow \lim_{x\rightarrow \propto } (1+sin^{2}x)

plz tell where's my mistake

21
Shubhodip ·

is my answer correct?

given expression can be written as

x^4 (1/x2 + sin2x/x2)/ x2 (1 + sin x /x )2

putting limits

x^4(1/x2 )/x2 = x2 / x2 = 1

1
pritishmasti ............... ·

that is the problem...i don't know the answer

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