Final answer:
To solve the limit x→0 x^2 / tanx−Sinx without using L'Hospital's rule, simplify the expression using trigonometric identities and the small-angle approximation.
Step-by-step explanation:
To solve the limit Limx→0 x2 / tanx−Sinx without using L'Hospital's rule, we can simplify the expression using trigonometric identities.
First, we factor out a common factor from the numerator to get x2 / tanx - sinx = x2 / sinx(cosx - 1).
Next, we can use the small-angle approximation to simplify the expression further. When x is small, sinx is approximately equal to x, and cosx is approximately equal to 1. Therefore, the expression becomes x2 / (x(1 - 1)) = x.