Problem 817 (difficulty: 3/10)

\(\displaystyle \lim_{x\to0}\frac{2e^x+e^{-x}-3}{\sin 2x+x^2+\sh x}=? \qquad \lim_{x\to1}x^{\frac1{1-x}}=? \qquad \lim_{x\to1}(2-x)^{\tg\frac{\pi x}2}=? \qquad \lim_{x\to\infty}\frac{2x+\sin x}{2x-\cos x} =? \)

Can we use the L'Hospital rule? Can we use the definition of the derivative at \(\displaystyle 0\) (or \(\displaystyle 1\))?

Give me another random problem!