a. Use the definition \( m_{\tan }=\lim _{h \rightarrow 0} \frac{f(a+h)-f(a)}{h} \) to find the slope of the line tangent to the graph of \( f \) at \( P \). Online Assignment 2-Abdulaziz Jahdali (b. Determine an equation of the tangent line at \( P \). 10. \( f(x)=x^{2}+1, P(-2,5) \) a. \( m_{\tan }=\square \) b. \( y=\square \)

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 \( x^{3}-3 x y+y^{3}=1 \)

Установите сходимость или расходимость указанных рядов с помощью интегрального признака Коши. \( \begin{array}{lll}\text { 1) } \frac{1}{2 \ln 2}+\frac{1}{3 \ln 3}+\ldots+\frac{1}{(n+1) \ln (n+1)}+\ldots \\ \text { 2) } \frac{1}{2 \ln ^{2} 2}+\frac{1}{3 \ln ^{2} 3}+\ldots+\frac{1}{(n+1) \ln ^{2}(n+1)}+\ldots ; \\ \sum_{n=1}^{\infty} \frac{\ln (n+1)}{(n+1)^{2}} ; & \text { 4) } \sum_{n=2}^{\infty} \frac{1}{\sqrt{n}} \cdot \ln \frac{n+1}{n-1} ; & \text { 5) } \sum_{n=1}^{\infty} \frac{1}{(n+1) \ln (n+1) \ln \ln (n+1)}\end{array} \)

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) \( \lim _{x \rightarrow 0^{-}} g^{\prime}(x)=-4 ; \lim _{x \rightarrow 0^{+}} g^{\prime}(x)=4 \)

\( L ( \sinh ( a t + b ) ) \)