If lim sin2x + asinx/x^3 exists, then the value of 'a' is?
- 2
- -2
- does not exist
- -1
Explanation
To evaluate the limit, we can start by rewriting the expression as:
lim (sin(2x) + a*sin(x)) / x^3
As x approaches 0, the sine functions can be approximated by their arguments, so we get:
lim (2x + a*x) / x^3 = lim (2 + a) / x^2
For this limit to exist, the numerator must be 0, so we set 2 + a = 0, which gives a = -2.
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