Derivative

Let $X(\omega)$ be the Fourier transform of the signal $x(t) = e^{-t^4} \cos t$, $-\infty < t < \infty$. The value of the derivative of $X(\omega)$ at $\omega=0$ is ________ (round...

Let $$f(x) = \int\limits_0^x {{e^t}(t - 1)(t - 2)dt} $$. Then f(x) decreases in the interval.

If $$f(0)=2$$ and $$f'\left( x \right) = {1 \over {5 - {x^2}}},$$ then the lower and upper bounds of $$f(1)$$ estimated by the mean value theorem are ______.

If $$f(t)$$ is the step-response of a linear time-invariant system, then its impulse response is given by ___________