What is the limit as x approaches infinity of ((sin(x)-cos(x)))/x ?

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

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limit as x approaches infinity of ((sin(x)-cos(x)))/x

x \to \infty lim (\frac{( sin ( x ) - cos ( x ) )}{x})

0

Solution steps

x \to \infty lim (\frac{sin ( x ) - cos ( x )}{x})

Expand

\frac{sin ( x ) - cos ( x )}{x} : \frac{sin ( x )}{x} - \frac{cos ( x )}{x}

= x \to \infty lim (\frac{sin ( x )}{x} - \frac{cos ( x )}{x})

x \to a lim [f (x) \pm g (x)] = x \to a lim f (x) \pm x \to a lim g (x)

With the exception of indeterminate form

= x \to \infty lim (\frac{sin ( x )}{x}) - x \to \infty lim (\frac{cos ( x )}{x})

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

x \to \infty lim (\frac{cos ( x )}{x}) = 0

= 0 - 0

Simplify

= 0

t \to 0 + lim (cos (t))

h \to 0 lim (\frac{( x + h ) ^{3} - 3}{h})

x \to \infty lim (\frac{u ( x ) k + 1}{u ( x ) k})

x \to \frac{π}{2} lim (ln ∣ cos (x) ∣)

x \to 4 lim (\frac{2 - 7 x}{4 - x})

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