2.3 Limit laws; Questions 83-86

[Eigenvalue]

Use the limit laws to evaluate each function
83. [tex]\lim_{x \to 0}4x²-2x+3[/tex]

84.[tex]\lim_{x \to 1} \frac{x³+3x²+5}{4-7x}[/tex]

85.[tex]\lim_{x \to -2} \sqrt{x²-6x+3}[/tex]

86. [tex]\lim_{x \to -1}(9x+1)²[/tex]

[Eigenvalue]

83. [tex]\lim_{x \to 0}4x²-2x+3[/tex]
=[tex]\lim_{x \to 0}4x²[/tex]-[tex]\lim_{x \to 0}2x[/tex]+[tex]\lim_{x \to 0}3[/tex]
=4(0)²-2(0)+3
=3

84.[tex]\lim_{x \to 1} \frac{x³+3x²+5}{4-7x}[/tex]
=[tex]\frac{ \lim_{x \to 1}x³+ \lim_{x \to 1}3x²+ \lim_{x \to 1}5}{ \lim_{x \to 1}4- \lim_{x \to 1}7x }[/tex]

=[tex]\frac{1³+3(1)²+5}{4-7(1)}[/tex]

=-3

85.[tex]\lim_{x \to -2} \sqrt{x²-6x+3}[/tex]
=[tex]\sqrt{ \lim_{x \to -2}x²- \lim_{x \to -2}6x+ \lim_{x \to -2}3 }[/tex]

=[tex]\sqrt{(-2)²-6(-2)+3}[/tex]

=[tex]\sqrt{19}[/tex]

86. [tex]\lim_{x \to -1}(9x+1)²[/tex]
=([tex]\lim_{x \to -1}9x[/tex]+[tex]\lim_{x \to -1}1[/tex])²
=(9(-1)+1)²
=(-8)²
=64