Given \( f(x)=5 x-9 \), then find \( \frac{F(2+h)-F(2)}{h} \)

1. Prove that under the transformation of independent variable \( x= \) \( \varphi(t) \), an \( n^{\text {th }} \)-order linear differential equation remains an \( n^{\text {th }} \)-order linear differential equation, and a homogeneous linear differential equation remains a homogeneous linear differential equation. Here \( x=\varphi(t) \) has continuous derivatives up to order \( n \) and \( \varphi^{\prime}(t) \neq 0 \).

\( \lim _ { n \rightarrow \infty } \frac { n \cdot \sin \frac { 1 } { n } - \cos \frac { 1 } { n } } { \ln ( 1 + \frac { 1 } { n ^ { 2 } } ) } \)

Soit \( \left(u_{n}\right) \) la sulte definie par On pose: \( V n \in \mathrm{~N} \); \( v_{n}=\frac{1}{u_{n-1}^{\prime}} \) H. Montrer que: \( (\mathrm{V} \sim \mathrm{N}): u_{n}>1 \). 2. Etudier la monotonie de la suite \( \left(u_{n}\right) \)

Discur the convergene at \( [1,2] \) given that \( f(x)=x^{3}-x-1 \)

If \( y=\frac{10-\cos x}{x} \), then simplify completely \( x \frac{d^{2} y}{d x^{2}}+2 \frac{d y}{d x} \)