Do not use a calculator for this problem. Find the \( x \)-value where the maximum value of \( y=\sin x-x^{2} \) occurs. When you need to solve for an expression equal to zero, use Newton's method with \( x=0 \) as your first guess and enter your second guess as the answer. Enter your answer as a traction. Submit Question Jump to Answer

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

Proporre un esempio di funzione \( g(x) \) tale che \[ \lim _{x \rightarrow+\infty} \frac{g(x)}{3 \log ^{2} x+1}=+\infty \]

\( ( e ^ { x } - \sin y ) d x + ( \cos y ) d y \)

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

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.