L' Hopital is invalid

Calculus Level 2

lim x 0 [ x n s i n ( 1 x ) ] = ? ? \huge \lim_{x\rightarrow 0} {\left[x^n\cdot sin\left(\frac{1}{x}\right)\right]=??}

  • Here n N n\in\mathbb {N}
-1 1 None of them n Can't be determined 0

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1 solution

Sanath Kamath
Jan 16, 2018

Let's plug in zero. lim x 0 n s i n ( 1 / 0 ) \lim_{x\to\infty} 0^n*sin(1/0) 0^n is 0 so therefore it's limit at zero is zero because zero multiplied by anything is zero.

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