What is the value of the sin3x/6x; as x approaches to zero

Using limits, it is found that the value of the function is of 0.5.

The limit given is:

The following property is used:

Hence, multiplying the numerator and denominator by 0.5:

The value of the function is of 0.5.

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Step-by-step explanation:

When x = 0,

sin3x / 6x = 0 / 0, which is an indeterminate form.

Hence we use L'Hospital's rule:

d/dx (sin3x) = 3cos3x

d/dx (6x) = 6

Now we have 3cos3x / 6 or 0.5cos3x.

When x = 0, 0.5cos3x = 0.5(1) = 0.5.

Hence the limit is 0.5.