80014 If \(f(x)=\int_{-1}^{x}|t| d t, x \geq(-1)\), then

80015 Let \(f(\mathrm{x})\) be a differentiable function in [2,7]. \(f(2)\) \(=3\) and \(f^{\prime}(x) \leq 5\) for all \(x\) in \((2,7)\), then the maximum possible value of \(f(x)\) at \(x=7\) is

80017 Let \([x]\) denotes the greatest integer less than or equal to \(x\). Then, the value of \(\alpha\) for which the function \(f(x)=\left\{\begin{array}{l}\frac{\sin \left[-x^{2}\right]}{\left[-x^{2}\right]}, x \neq 0 \\ \alpha, \quad x=0\end{array}\right.\) is continuous at \(\mathbf{x}=\mathbf{0}\), is

80019 Let \(f: R \rightarrow R\) be a continuous function which satisfies \(f(x)=\int_{0}^{x} f(t) d t\). Then, the value of \(f\) \(\left(\log _{e} 5\right)\) is

80014 If \(f(x)=\int_{-1}^{x}|t| d t, x \geq(-1)\), then

80015 Let \(f(\mathrm{x})\) be a differentiable function in [2,7]. \(f(2)\) \(=3\) and \(f^{\prime}(x) \leq 5\) for all \(x\) in \((2,7)\), then the maximum possible value of \(f(x)\) at \(x=7\) is

80017 Let \([x]\) denotes the greatest integer less than or equal to \(x\). Then, the value of \(\alpha\) for which the function \(f(x)=\left\{\begin{array}{l}\frac{\sin \left[-x^{2}\right]}{\left[-x^{2}\right]}, x \neq 0 \\ \alpha, \quad x=0\end{array}\right.\) is continuous at \(\mathbf{x}=\mathbf{0}\), is

80019 Let \(f: R \rightarrow R\) be a continuous function which satisfies \(f(x)=\int_{0}^{x} f(t) d t\). Then, the value of \(f\) \(\left(\log _{e} 5\right)\) is

80014 If \(f(x)=\int_{-1}^{x}|t| d t, x \geq(-1)\), then

80015 Let \(f(\mathrm{x})\) be a differentiable function in [2,7]. \(f(2)\) \(=3\) and \(f^{\prime}(x) \leq 5\) for all \(x\) in \((2,7)\), then the maximum possible value of \(f(x)\) at \(x=7\) is

80017 Let \([x]\) denotes the greatest integer less than or equal to \(x\). Then, the value of \(\alpha\) for which the function \(f(x)=\left\{\begin{array}{l}\frac{\sin \left[-x^{2}\right]}{\left[-x^{2}\right]}, x \neq 0 \\ \alpha, \quad x=0\end{array}\right.\) is continuous at \(\mathbf{x}=\mathbf{0}\), is

80019 Let \(f: R \rightarrow R\) be a continuous function which satisfies \(f(x)=\int_{0}^{x} f(t) d t\). Then, the value of \(f\) \(\left(\log _{e} 5\right)\) is

80014 If \(f(x)=\int_{-1}^{x}|t| d t, x \geq(-1)\), then

80015 Let \(f(\mathrm{x})\) be a differentiable function in [2,7]. \(f(2)\) \(=3\) and \(f^{\prime}(x) \leq 5\) for all \(x\) in \((2,7)\), then the maximum possible value of \(f(x)\) at \(x=7\) is

80017 Let \([x]\) denotes the greatest integer less than or equal to \(x\). Then, the value of \(\alpha\) for which the function \(f(x)=\left\{\begin{array}{l}\frac{\sin \left[-x^{2}\right]}{\left[-x^{2}\right]}, x \neq 0 \\ \alpha, \quad x=0\end{array}\right.\) is continuous at \(\mathbf{x}=\mathbf{0}\), is

80019 Let \(f: R \rightarrow R\) be a continuous function which satisfies \(f(x)=\int_{0}^{x} f(t) d t\). Then, the value of \(f\) \(\left(\log _{e} 5\right)\) is