10. \( f(x)=4 x^{6} \sqrt{x+10} \)

6 A curve is such that \( \frac{d y}{d x}=\frac{4}{\sqrt{2 x+k}} \), where \( k \) lo a constant. The point \( P(3,2) \) lies on the curve and tho norma! to the curve at \( P \) is \( x+4 y=11 \). Find the equation of the eurve.

The series \( \sum_{k=1}^{\infty}(-1)^{k} \frac{k^{k}}{(k+2)^{k+1}}: \) converged but not absolutly converges Absolutly converges Diverges conditionaly converges

\( \int 4 e^{-6 x} d x \) (use substitution: \( u=-6 x \) )

\( \int \frac{\cos x}{\sin ^{2} x} \mathrm{dx} \) (use substitution: \( u=\sin x \) )

The series \( \sum_{\substack{k=1}}^{\infty} \frac{(-1)^{k}}{\sqrt{k}} \) converges. True False