Question

1. Solve y = 5e^3x + sin x (dy/dx)
2. The velocity of a body as a function of time is given as ν (t) = 5e ^-2t  + 4, where t is in seconds, and v is in m/s. Solve the acceleration in m/s² at t = 0.6

Answer 1

1.

$$\dfrac{dy}{dx}=\dfrac{d}{dx}(5e^{3x}+\sin x)=15e^{3x}+\cos x$$

2.

$$a(t)=\dfrac{dv}{dt}=\dfrac{d}{dt}(5e^{-2t}+4)=-10e^{-2t}$$

$$a(0.6)=-10e^{-2(0.6)}\ m/s^2$$

$$=-10e^{-1.2}\ m/s^2\approx-3.012\ m/s^2$$