Evaluate the integral \( \int(2 x+5)\left(x^{2}+5 x+5\right)^{5} d x \) by making the substitution \( u=x^{2}+5 x+5 \) \( +C \)

s] Using calculus and showing all working, graph the function \[ f(x)=\frac{x+2}{x^{2}-1} \]

5. [12 marks] Using calculus and showing all your working, sketch the function \[ f(x)=\frac{x}{x^{2}-4} \] noting the domain of \( f(x) \), any intercepts or asymptotes, symmetry, regions where the function is increasing or decreasing and any relative extrema. Note: You don't have to consider the second derivative and concavity.

\( \lim _ { n \rightarrow + \infty } \frac { n ^ { 5 } + \sin n } { 3 ( \arctan n ) n ^ { 5 } } \)

Gegeben ist eine weitere Funktion h. mit der Gleichung \( h(x)=0,5 x^{3}-4 x^{2}+6 x+2 \) 74 a) Untersuchen Sie den Graphen von \( h \) auf mögliche Wendepunkte.

Decide whether the following statement is true or false. The cube function is odd and is increasing on the interval \( (-\infty, \infty) \). Choose the correct answer below. False True