What is the limit as x approaches 0 of (sin(x)-cos(x)sin(x))/(x^2) ?

The limit as x approaches 0 of (sin(x)-cos(x)sin(x))/(x^2) is 0

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limit as x approaches 0 of (sin(x)-cos(x)sin(x))/(x^2)

x \to 0 lim (\frac{sin ( x ) - cos ( x ) sin ( x )}{x ^{2}})

0

Solution steps

x \to 0 lim (\frac{sin ( x ) - cos ( x ) sin ( x )}{x ^{2}})

x \to a - lim f (x) = x \to a + lim f (x) = L

then

x \to a lim f (x) = L

x \to 0 - lim (\frac{sin ( x ) - cos ( x ) sin ( x )}{x ^{2}}) = 0

x \to 0 + lim (\frac{sin ( x ) - cos ( x ) sin ( x )}{x ^{2}}) = 0

= 0

x \to 0 + lim ((x^{2} + 1)^{\frac{1}{x}})

x \to 0 + lim (\frac{sin ( x ^{2} )}{x})

\frac{d y}{d x} - 2 x y = e^{x^{2}}

x (\frac{d y}{d x}) + y = y^{2}

\int \frac{3 - 18 x}{64 - 9 x ^{2}} d x

What is the limit as x approaches 0 of (sin(x)-cos(x)sin(x))/(x^2) ?
The limit as x approaches 0 of (sin(x)-cos(x)sin(x))/(x^2) is 0