Suppose that the velocity \( v(t) \) (in meters per second) of a sky diver falling near the Earth's surface is given by the following exponential function, where time \( t \) is the time after diving measured in seconds. \[ v(t)=74-74 e^{-0.19 t} \] How many seconds after diving will the sky diver's velocity be 61 meters per second? Round your answer to the nearest tenth, and do not round any intermediate computations. seconds

Residues at Poles = Proof the Theorem Assume \( f(z) \) has the following form \[ f(z)=\frac{\phi(z)}{\left(z-z_{0}\right)^{m}} \] where \( \varphi(\mathrm{z}) \) is analytic and nonzero at \( \mathrm{z}_{0} \), then it has Taylor series representation

Residues at Poles - Example 1 The function \( \quad f(z)=\frac{z+1}{z^{2}+9} \) has an isolated singular point at \( \mathrm{z}=3 \mathrm{i} \) and can be written

Find the derivative of \( f(w)=\frac{3}{\left(w^{2}-6\right)^{5}} \)

(c) \( \int_{6}^{0}(2+5 x) e^{\frac{1}{3} x} d x \)

احسب التكامل لـ \( \frac{4x^3 - 7x + 5}{2x + 1} dx \) من خلال تطبيق طريقة القسمة الطويلة.