\(\sin^{-1}x+\sin^{-1}y=\) (principal values)
For \(x\in[-1,1]\), evaluate \(\ \sin\!\big(2(\sin^{-1}x+\cos^{-1}x)\big)\).
For \(x\in\mathbb{R}\), compute \(\csc\!\big(\tan^{-1}x+\cot^{-1}x\big)\).
If \(|x|\ge1\), then \(\tan\!\left[\dfrac{2}{3}\big(\tan^{-1}x+\cot^{-1}x\big)\right]=\) ?
\(\dfrac{d}{dx}\big(e^{x}+\cos5x\big)=\) ?
\(\dfrac{d}{dx}\!\left(\dfrac{1}{4}\sec4x\right)=\) ?
\(\dfrac{d}{dx}\big(\log_{e}(10x)\big)=\) ?
\(\displaystyle \int \sin\!\left(\frac{3x}{4}\right)\,dx=\) ?
\(\displaystyle \int \cos\!\left(\frac{7x}{9}\right)\,dx=\) ?
\(\displaystyle \int \sec^{2}\!\left(\frac{17x}{23}\right)\,dx=\) ?
\(\displaystyle \int 4^{x}\,dx=\) ?
\(\displaystyle \int x\,(4x^{2}-6)\,dx=\) ?
\(\displaystyle \int e^{x}(\cos x-\sin x)\,dx=\) ?
\(\displaystyle \int e^{x}\,(x^{3}+3x^{2})\,dx=\) ?
\(\displaystyle \int e^{x}\!\left(\frac{1}{x}-\frac{1}{x^{2}}\right)\,dx=\) ?
\(3\vec{k}\cdot(13\vec{i}-7\vec{k})=\) ?
\(\dfrac{d}{dx}\big(\sin \tfrac{4x}{5}\big)=\) ?
\(\big(3\vec{i}-4\vec{k}\big)^{2}=\) ?
\((\vec{i}-\vec{j}+\vec{k})\cdot(7\vec{i}-8\vec{j}+9\vec{k})=\) ?
If the line \(\dfrac{x}{-1}=\dfrac{y}{2}=\dfrac{z}{3}\) is parallel to the plane \(ax+by+cz+d=0\) then
\((11\vec{i}-7\vec{j}-\vec{k})\cdot(8\vec{i}-\vec{j}-5\vec{k})=\) ?
If \(P(A)=\dfrac{7}{11},\ P(B)=\dfrac{9}{11},\ P(A\cap B)=\dfrac{4}{11}\), then \(P(A/B)=\) ?