lim_{x \to 0} \frac{\sin^2(\frac{x}{2})}{x^2} = lim_{x \to 0} \left(\frac{\sin(\frac{x}{2})}{\frac{x}{2}}\right)^2 * \frac{1}{4}
You asked:
Solve the equation \(\lim_{x \to 0}{\frac{{\sin\left( \frac{x}{2} \right)}^{2}}{{x}^{2}}} = \lim_{x \to 0}{{\left( \frac{\sin\left( \frac{x}{2} \right)}{\frac{x}{2}} \right)}^{2} \cdot \frac{1}{4}}\) for the variable \(x\).
MathBot Answer:
This equation has no unknown quantities, so it is either true or false.
This equation is true because the left-hand side is equal to the right-hand side.
The left-hand side of the equation is:
\[\lim_{x \to 0}{\frac{{\sin\left( \frac{x}{2} \right)}^{2}}{{x}^{2}}} = \frac{1}{4}\]The right-hand side of the equation is:
\[\lim_{x \to 0}{{\left( \frac{\sin\left( \frac{x}{2} \right)}{\frac{x}{2}} \right)}^{2} \cdot \frac{1}{4}} = \frac{1}{4}\]