Calculate the area enclosed between the lines \( y = 2x + 3 \) and \( y = x^2 \).

22. a) If \( f(x)=\frac{|6-x|}{x-6} \), find \( \lim _{x \rightarrow 6+} f(x) \) (if exist.) b) Evaluate: \( \lim _{x \rightarrow 0} \frac{\tan x-\sin x}{x^{3}} \) c) Evaluate: \( \lim _{x \rightarrow 0} \frac{x\left(2^{2}-1\right)}{1-\cos x} \) KMC Note d) Find \( \frac{d x}{d y} \) if \( x^{3}+y^{3}=3 a x^{2} y \) e) What is the derivative of \( \sec ^{-1} x \) with respect to ' \( x \) '.

\( \frac{d}{dx}\frac{1}{sin^{2}x} \)

Let \( x y+e^{x}-e^{y}=0 \), then \( y^{\prime}(0)= \)

If \( x^{3}+y^{3}=6 x y \), then find \( \frac{d y}{d x} \) and \( \frac{d^{2} y}{d x^{2}} \)

Let \( y=\sin x \cdot \cos x \), then \( d y= \)