Evaluate Limit 1

Calculus Level 1

lim ⁡ x → 0 ( 1 sin ⁡ x − 1 x ) = ? \large\displaystyle\lim_{x \to 0} \left(\dfrac{1}{\sin x} - \dfrac{1}{x}\right) = \, ?


The answer is 0.

Md Zuhair by Md Zuhair , 20, India

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1 solution

substitute to x a number near to zero, say x = 0.00001

1 s i n 0.00001 \frac{1}{sin 0.00001} − - 1 / 0.00001 1/0.00001 = = 100000 − 100000 100000 - 100000 = = 0 0

note: s i n 0.000001 sin 0.000001 must be in the radian mode of your calculator

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