What is the limit as x approaches 0 of [x]*sin(1/x) ?

The limit as x approaches 0 of [x]*sin(1/x) is 0

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limit as x approaches 0 of [x]*sin(1/x)

x \to 0 lim ([x] \cdot sin (\frac{1}{x}))

0

Solution steps

x \to 0 lim ([x] sin (\frac{1}{x}))

Simplify

= x \to 0 lim (x sin (\frac{1}{x}))

Apply the Squeeze Theorem:

0

= 0

\int \frac{7 x ^{2} + 8 x - 2}{x ^{2} + 2 x} d x

z \to (2 i) lim (z^{2} - z)

d er i v a t i v e f (x) = 2^{x} lo g_{2} (x)

t an g e n t f (x) = 6 - x, at x = 3

\int x^{2} e^{- 6 x} d x

What is the limit as x approaches 0 of [x]*sin(1/x) ?
The limit as x approaches 0 of [x]*sin(1/x) is 0