lim as x –> 0 sinax/sinbx
a/b
In order to find the limit, we have to use the following trigonometric identity:
lim as z –> 0 sin z / z = 1
Let z = ax, and substitute into the expression above:
lim as x –> 0 sin ax / sin bx = lim as x –> 0 a sin(ax) / (ax) / b sin(bx) / bx
Now we can apply the trigonometric identity and simplify:
lim as x –> 0 a / b * (sin(ax) / ax) / (sin(bx) / bx) = a / b * 1 / 1 = a / b
Therefore, the limit as x approaches 0 of sin(ax) / sin(bx) is equal to a / b.
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