(b) \( \lim _{x \rightarrow+\infty} \log x-\sqrt{x} \)

\( y=arctan\sqrt {x} \)

\( \lim _ { x \rightarrow 1 } ( \frac { \sqrt[ 4 ] { x } + \sqrt[ 3 ] { x } + \sqrt { x } - 3 } { x - 1 } ) ^ { n } \)

lizando el método de separación de variables, resuelve el siguiente p ma de contorno \( \left\{\begin{array}{l}\frac{\partial^{2} u(x, y)}{\partial x^{2}}+\frac{\partial^{2} u(x, y)}{\partial y^{2}}=0, \quad-1<x<1,-1<y<1 \\ u(-1, y)=0 \quad, \quad u(1, y)=\cos \left(\frac{\pi y}{2}\right), \quad-1<y<1 \\ u(x,-1)=0 \quad, \quad u(x, 1)=\operatorname{sen}(\pi x), \quad-1<x<1\end{array}\right. \)

Example: Compute the slope of the tangent line to the parabola \( y=x^{2} \) at the point \( \mathrm{P}(1,1) \).

\( y=\sqrt{x} \) at \( x_{0}=1, x_{0}=4 \)