What is the limit as x approaches infinity of (sin(x-3))/(x-3) ?

The limit as x approaches infinity of (sin(x-3))/(x-3) is 0

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limit as x approaches infinity of (sin(x-3))/(x-3)

x \to \infty lim (\frac{sin ( x - 3 )}{x - 3})

0

Solution steps

x \to \infty lim (\frac{sin ( x - 3 )}{x - 3})

Apply the Squeeze Theorem:

0

= 0

x \to \infty lim (\frac{1}{arctan ( x )})

x \to 0 lim (\frac{sinh ( 2 x )}{x})

x \to a lim (\frac{x ^{5} - a ^{5}}{x ^{4} - a ^{4}})

x \to \infty lim (\frac{3 x - cos ( x )}{2 x + sin ( x )})

x \to \infty lim (\frac{4 x ^{2} + 5 x - 1}{x ^{2} - 7 x + 29})

What is the limit as x approaches infinity of (sin(x-3))/(x-3) ?
The limit as x approaches infinity of (sin(x-3))/(x-3) is 0