Question-108498

Question Number 108498 by mohammad17 last updated on 17/Aug/20

Answered by Aziztisffola last updated on 17/Aug/20

1) y = {(x + 2)}^{x} = e^{xln (x + 2)}

\frac{dy}{dx} = (\ln (x + 2) + \frac{x}{x + 2}) {(x + 2)}^{x}

\frac{dy}{dx} (- 1) = - 1

Commented by mohammad17 last updated on 17/Aug/20

t h a n k y o u s i r

Answered by Aziztisffola last updated on 17/Aug/20

3) {xy}^{'} + y = e^{x} \Rightarrow y^{'} + \frac{1}{x} y = \frac{e^{x}}{x}

I . F = e^{\int \frac{dx}{x}} = e^{\ln ∣ x ∣} = x

yx = \int \frac{e^{x}}{x} xdx = e^{x} + C

y = \frac{e^{x}}{x} + \frac{C}{x}

4) ch (5 x) + sh (5 x) = e^{5 x}

\int \frac{dx}{ch (5 x) + sh (5 x)} = \int \frac{dx}{e^{5 x}} = \int e^{- 5 x} dx

= - \frac{1}{5} e^{- 5 x} + C

5) \vec{V_{1}} (1; 1; 1) and \vec{V_{2}} (1; 1; - 2)

\vec{V_{1}} . \vec{V_{2}} = 1 + 1 - 2 = 0 \Rightarrow \vec{V_{1}} ⊥ \vec{V_{2}}

Commented by mohammad17 last updated on 17/Aug/20

t h a n k y o u s i r