\( L = \int _ { 0 } ^ { 3 } \frac { \sqrt { ( x + 1 ) ^ { 2 } + 1 } } { x + 1 } d x \)

\( \lim _ { x \rightarrow 0 } \frac { 3 ( x - \operatorname { cts } x ) } { x } \)

7. Find \( \lim _{x \rightarrow 2} \frac{\sqrt{6-x}-2}{\sqrt{3-x}-1} \) 8. If \( f(x)=x^{2}+10 \sin x \), show that there is a number \( c \) such that \( f(x)=1000 \)

Suppose \( f \) is continuous on \( [1,5] \) and the only solutions of the equation \( f(x)= \) 6 are \( x=1 \) and \( x=4 \). If \( f(2)=8 \), explain why \( f(3)>6 \). Show that \( F(x)=|x| \) is continuous evervwhere.

By using Newton-Raphson Method, determine the root for \( x^{3}+2 x^{2}-1=0 \). Given \( x_{0}=0.5 \). Give the answer correct to four decimal places. Dengan mengomenan

Show that \( F(x)=|x| \) is continuous everywhere.