Find the limit of the polynomial \( p(x) \) as \( x \) approaches \( -\infty \) \[ p(x)=4 x^{7}-7 x^{6}+1 \] The limit of \( p(x) \) as \( x \) approaches \( -\infty \) is

11. Sia data la funzione \( f \), derivabile in \( \mathbb{R} \), tale che \( f(0)=-5, f^{\prime}(0)=-4 \). Allora \( g(x)=|f(x)| \) a) \( g(x) \) presenta un punto angoloso in \( x=0 \) b) \( P(0,5) \in g(x) \) e \( g^{\prime}(0)=-4 \) c) \( g \) è derivabile in \( x=0 \) e \( g^{\prime}(0)=4 \) d) \( g \) è derivabile in \( x=0 \) e \( g^{\prime}(0)=-4 \) e) \( \lim _{x \rightarrow 0^{-}} g^{\prime}(x)=-4 ; \lim _{x \rightarrow 0^{+}} g^{\prime}(x)=4 \)

In exercises 18 to 22 , find the limit, If the limit does not exist, justify your answe (18) Limit of the function \( f(x)=\frac{|x-3|}{x-3} \) as \( x \) tends to 3 )rom the right:

Find \( \frac{d^{2} y}{d x^{2}} \) given \( x^{3}-3 x y+y^{3}=1 \)

Исследовать на сходимость ряды с положительными членами \( \sum_{n=1}^{\infty} \frac{(n+2)!}{n^{n}} \). \( \sum_{n=1}^{\infty} \frac{n+3}{n(n+1)} \)

\( \lim _ { x \rightarrow a } ( a - x ) \tan ( \frac { x x } { 20 } ) \)