5.) -4
6.) 0
5.) [tex]\underset{x\rightarrow-1}{\lim}\;\dfrac{x^2-2x-3}{x^2+3x+2}[/tex]
[tex]\underset{x\rightarrow-1}{\lim}\;\dfrac{x^2-2x-3}{x^2+3x+2}[/tex]
[tex]\Rightarrow\underset{x\rightarrow-1}{\lim}\;\dfrac{x^2-3x+x-3}{x^2+2x+x+2}[/tex]
[tex]\Rightarrow\underset{x\rightarrow-1}{\lim}\;\dfrac{x(x-3)+(x-3)}{x(x+2)+(x+2)}[/tex]
[tex]\Rightarrow\underset{x\rightarrow-1}{\lim}\;\dfrac{(x+1)(x-3)}{(x+1)(x+2)}[/tex]
[tex]\Rightarrow\dfrac{(-1)-3}{(-1)+2}[/tex]
[tex]\Rightarrow-\dfrac{4}{1}\;\;\;=-4[/tex]
6. ) [tex]\underset{x\rightarrow0}{\lim}\;\dfrac{5x^3}{2x^2-3x}[/tex]
[tex]\underset{x\rightarrow0}{\lim}\;\dfrac{5x^3}{2x^2-3x}[/tex]
[tex]\Rightarrow \underset{x\rightarrow0}{\lim}\;\dfrac{x\cdot5x^2}{x(2x-3)}[/tex]
[tex]\Rightarrow \underset{x\rightarrow0}{\lim}\;\dfrac{5x^2}{2x-3}[/tex]
[tex]\Rightarrow \dfrac{5(0)}{2(0)-3}[/tex]
[tex]\Rightarrow \dfrac{0}{-3}\;\;\;=0[/tex]
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