80220 The function \(f(x)=x-[x]\) where [ ] denotes the greatest integer function is

80221 Let \(f:[0,1] \rightarrow \mathrm{R}\) (the set of all real numbers) be a function. Suppose the function \(f\) is twice differentiable, \(f(0)=f(1)=0\) and satisfies \(f^{\prime \prime}(x)-2 f^{\prime}(x)+f(x) \geq e^{x}, x \in[0,1]\). If the function \(\mathrm{e}^{-\mathrm{x}} f(\mathrm{x})\) assumes its minimum in the interval \([0,1]\) at \(x=\frac{1}{4}\), which of the following is true?

80222 If \(x \sin (\alpha+y)=\sin y\) and \(y=\frac{m}{x^{2}+2 n x+1}\), then \(\mathbf{m}^{2}=\)

80223 The number of points in the interval \((0,2)\) at which \(\quad f(x)=|x-0.5|+|x-1|+\tan x \quad\) is not differentiable is

80220 The function \(f(x)=x-[x]\) where [ ] denotes the greatest integer function is

80221 Let \(f:[0,1] \rightarrow \mathrm{R}\) (the set of all real numbers) be a function. Suppose the function \(f\) is twice differentiable, \(f(0)=f(1)=0\) and satisfies \(f^{\prime \prime}(x)-2 f^{\prime}(x)+f(x) \geq e^{x}, x \in[0,1]\). If the function \(\mathrm{e}^{-\mathrm{x}} f(\mathrm{x})\) assumes its minimum in the interval \([0,1]\) at \(x=\frac{1}{4}\), which of the following is true?

80222 If \(x \sin (\alpha+y)=\sin y\) and \(y=\frac{m}{x^{2}+2 n x+1}\), then \(\mathbf{m}^{2}=\)

80223 The number of points in the interval \((0,2)\) at which \(\quad f(x)=|x-0.5|+|x-1|+\tan x \quad\) is not differentiable is

80220 The function \(f(x)=x-[x]\) where [ ] denotes the greatest integer function is

80221 Let \(f:[0,1] \rightarrow \mathrm{R}\) (the set of all real numbers) be a function. Suppose the function \(f\) is twice differentiable, \(f(0)=f(1)=0\) and satisfies \(f^{\prime \prime}(x)-2 f^{\prime}(x)+f(x) \geq e^{x}, x \in[0,1]\). If the function \(\mathrm{e}^{-\mathrm{x}} f(\mathrm{x})\) assumes its minimum in the interval \([0,1]\) at \(x=\frac{1}{4}\), which of the following is true?

80222 If \(x \sin (\alpha+y)=\sin y\) and \(y=\frac{m}{x^{2}+2 n x+1}\), then \(\mathbf{m}^{2}=\)

80223 The number of points in the interval \((0,2)\) at which \(\quad f(x)=|x-0.5|+|x-1|+\tan x \quad\) is not differentiable is

80220 The function \(f(x)=x-[x]\) where [ ] denotes the greatest integer function is

80221 Let \(f:[0,1] \rightarrow \mathrm{R}\) (the set of all real numbers) be a function. Suppose the function \(f\) is twice differentiable, \(f(0)=f(1)=0\) and satisfies \(f^{\prime \prime}(x)-2 f^{\prime}(x)+f(x) \geq e^{x}, x \in[0,1]\). If the function \(\mathrm{e}^{-\mathrm{x}} f(\mathrm{x})\) assumes its minimum in the interval \([0,1]\) at \(x=\frac{1}{4}\), which of the following is true?

80222 If \(x \sin (\alpha+y)=\sin y\) and \(y=\frac{m}{x^{2}+2 n x+1}\), then \(\mathbf{m}^{2}=\)

80223 The number of points in the interval \((0,2)\) at which \(\quad f(x)=|x-0.5|+|x-1|+\tan x \quad\) is not differentiable is