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\[ \large \lim_{ x\to \infty }x \sin \left (\dfrac { 1 }{ x }\right ) = \, ? \]

\[ \large \lim_{ x\to-\infty }\dfrac { { e }^{ x }-{ e }^{ -x } }{ { e }^{ x }+{ e }^{ -x } } = \, ? \]

\[ \large \lim_{ x\to \infty }\dfrac { \sqrt [ 3 ]{ 8{ x }^{ 3 }+1 } }{ | x | } = \, ? \]

\[\] Notation: \( | \cdot | \) denotes the absolute value function.

\[ \large \lim_{ x\to -\infty }\dfrac { \sqrt { { 9x }^{ 2 }-5 } }{ 4x+3 } = \, ? \]

\[ \lim_{ x\to\infty }\dfrac { n{ x }^{ n }-{ (n-1)x }^{ n-1 }+{ (n-2)x }^{ n-2 }-\cdots+2{ x }^{ 2 }-x+3 }{ { nx }^{ n }+(n-1){ x }^{ n-1 }+\cdots+x+5 } = \, ? \]

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