What is the limit as x approaches 3 of x^2sin(1/x) ?

The limit as x approaches 3 of x^2sin(1/x) is 9sin(1/3)

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limit as x approaches 3 of x^2sin(1/x)

x \to 3 lim (x^{2} sin (\frac{1}{x}))

9 sin (\frac{1}{3})

Decimal

2.94475 \dots

Solution steps

x \to 3 lim (x^{2} sin (\frac{1}{x}))

Plug in the value

x = 3

= 3^{2} sin (\frac{1}{3})

Simplify

= 9 sin (\frac{1}{3})

x \to 3 lim (\frac{1}{( 1 - x ) ^{4}})

x \to 3 lim ((\frac{x}{x + 1})^{x})

x \to 3 lim (\frac{1}{( 1 - e ^{x} )})

x \to 3 lim (x^{7} ln (tan (x)))

x \to 3 lim (5 x \cdot cot^{2} (x))

What is the limit as x approaches 3 of x^2sin(1/x) ?
The limit as x approaches 3 of x^2sin(1/x) is 9sin(1/3)