Cuál es la longitud de arco de la curva dada por \( r(t)=\left(t^{3}+1\right) i+\left(t^{2}+2\right) j+(t-3) k \) en el intervalo \( [1,4] \) ?

If the slope of the tangent to the curve: \( y=f(x) \) at any point on it equals \( 6 x+a \), whe \( a \) is constant if the equation of the tangent to the curve at the point \( (1,-1) \) is \( y=4- \) \( 5 x \), then the equation of the curve is ... \( \begin{array}{llll}\text { a) } y=3 x^{2}-4 & \text { b) } y=3 x^{2}-11 x+7 & \text { c) } y=3 x^{2}-4 x & \text { d) } y=3 x^{2}-x-3\end{array} \)

(1) Find the value of: \( \quad \lim _{x \rightarrow 4} \frac{x^{3}-15 x-4}{x-4} \)

3. \( \lim _{x \rightarrow \infty} \frac{x-1}{2 x+5} \)

3. \( \lim _{x \rightarrow \infty} \frac{x-1}{2 x+5} \)

Determine the indefinite integral \( \int (6x^3 + 4x^2) \, dx \)