Question

The value of `lim_{x→2} (e^{3x - 6} - 1)/(sin(2 - x))` is ______ 

Options

• `3/2`

• 3

• -3

• -1

Answer 1

The value of `lim_{x→2} (e^{3x - 6} - 1)/(sin(2 - x))` is -3.

Explanation:

`lim_{x→2} (e^{3x - 6} - 1)/(sin(2 - x))` 

= `lim_{x→2} (e^{3(x - 2)} - 1)/(3(x - 2)) xx 1/((sin(2 - x))/(-3(2 - x)))`

= 1 × -3 ........`[∵ lim_{x→0} (e^x - 1)/x = 1, lim_{x→0} sinx/x = 1]`

= -3