What is the limit as x approaches 0 of (sin(a)x)/x ?

The limit as x approaches 0 of (sin(a)x)/x is sin(a)

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limit as x approaches 0 of (sin(a)x)/x

x \to 0 lim (\frac{sin ( a ) x}{x})

sin (a)

Solution steps

x \to 0 lim (\frac{sin ( a ) x}{x})

Cancel the common factor:

x

= x \to 0 lim (sin (a))

x \to a lim c = c

= sin (a)

x \to 0 + lim (arcsin (x - 1))

x \to 0 lim (x^{3} + \frac{cos ( 5 x )}{10000})

x \to 0 + lim (9 x ln (x))

x \to 4 lim (3 x^{2} + 2 x)

x \to 0 lim (\frac{x}{e ^{- \frac{8}{x}}})

What is the limit as x approaches 0 of (sin(a)x)/x ?
The limit as x approaches 0 of (sin(a)x)/x is sin(a)