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Grade 12Algebra

Solve the question given in the attached image............................................................
..............?.....

Question image for Solve the question given in the attached image...

Sarvesh

7 Years agoGrade 12

1 Answer

Omkar Doiphode

7 Years ago

$\lim_{x\rightarrow \infty}(1+xe^{\frac{-1}{x^{2}}}sin(\frac{1}{x^{4}}))$

$= 1 + \lim_{x\rightarrow \infty}(xe^{\frac{-1}{x^{2}}}sin(\frac{1}{x^{4}}))$

$= 1+ \lim_{x\rightarrow \infty}(xe^{\frac{-1}{x^{2}}}) \lim_{x\rightarrow \infty}(sin(\frac{1}{x^{4}})$

$=1+0.\lim_{x\rightarrow \infty}(sin(\frac{1}{x^{4}})$

Note that sine function is a bounded function, i.e. its value will always lie in the interval [-1,1]

$\lim_{x\rightarrow \infty}(sin(\frac{1}{x^{4}}) \in [-1,1]$

Hence value of given limit is 1+0=1

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