The radius of convergence of \[ \sum_{n=0}^{\infty}(4+3 i) z^{2 n+1} \] is

If the point \( (1,2) \) is an inflection point of the curve of the function \( f \) where \( f^{\prime}(x)=4 x^{3}-\mathrm{k} x^{2} \), then \( \mathrm{k}=\ldots \ldots \) (a) 24 (b) 6 (c) 4 (d) 12

Consider the parametric curve \( x=\cos \theta \) and \( y=\sin \theta \). Determine whether this curve is concave up, down, or neither at \( \theta=\frac{\pi}{6} \) A) upward B) downward C) neither D) All answers a b

4. DETERMINDR \( \quad \int^{\sqrt{4-x^{2}}} d x \).

Al resolver la integral doble \( \int_{1}^{2} \int_{1-x}^{\sqrt{x}} x^{2} y d y d x \) obtenemos: a. 402 b. 170 c. 170 d. \( 163 / 120 \)

¿Cuál es la longitud de la curva paramétrica \( r(x)=\left(4 t^{3}+7 t, 3 t^{2}-1,2 t^{3}-5 t^{2}+4 t\right. \) en el intervalo \( [0,2] \) ?