spain-selectividad 2018 Q2

spain-selectividad · Other · selectividad__madrid_matematicas-II_extraordinaria 2.5 marks Curve Sketching Continuity and Discontinuity Analysis of Piecewise Functions

Consider the function $f ( x ) = \left\{ \begin{array} { l l l } 8 e ^ { 2 x - 4 } & \text { if } & x \leq 2 \\ \frac { x ^ { 3 } - 4 x } { x - 2 } & \text { if } & x > 2 \end{array} \right.$ and it is requested:
a) (0.75 points) Study the continuity of $f$ at $x = 2$.
b) (1 point) Calculate the asymptotes of $f ( x )$. Is there any vertical asymptote?
c) (0.75 points) Calculate $\int _ { 0 } ^ { 2 } f ( x ) d x$

Consider the function $f ( x ) = \left\{ \begin{array} { l l l } 8 e ^ { 2 x - 4 } & \text { if } & x \leq 2 \\ \frac { x ^ { 3 } - 4 x } { x - 2 } & \text { if } & x > 2 \end{array} \right.$ and it is requested:

a) (0.75 points) Study the continuity of $f$ at $x = 2$.

b) (1 point) Calculate the asymptotes of $f ( x )$. Is there any vertical asymptote?

c) (0.75 points) Calculate $\int _ { 0 } ^ { 2 } f ( x ) d x$

Paper Questions

Q1 Q2 Q3 Q4