Multiple Choice Question (MCQ)
Find the value of \lim\limits_{x\to \infty } 2x\sin\Big( \dfrac{4}{x} \Big)
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×
2
-
×
4
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✓
8
-
×
\dfrac{1}{2}
Answer
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\lim\limits_{x\to \infty } 2x\sin\Big( \dfrac{4}{x} \Big)
=\lim\limits_{x\to \infty } 8\cdot \dfrac{\sin\Big( \dfrac{4}{x}\Big) }{\dfrac{4}{x}}
=\lim\limits_{x\to \infty } 8\cdot 1
=8
So C is the correcr choice
In this calculation, we used the basic limit
\lim\limits_{x\to0 }\dfrac{\sin x}{x} =1