2.3 Limit laws; Questions 87-92

[Eigenvalue]

Use direct substitution to evaluate each limit

87. [tex]\lim_{x \to 7}x²[/tex]

88. [tex]\lim_{x \to -2}4x²-1[/tex]

89. [tex]\lim_{x \to 0} \frac{1}{1+sin(x)}[/tex]

90. [tex]\lim_{x \to 2} e^{2x-x² }[/tex]

91. [tex]\lim_{x \to 1} \frac{2-7x}{x+6}[/tex]

92.[tex]\lim_{x \to 3}ln( e^{3x})[/tex]

[Eigenvalue]

87. [tex]\lim_{x \to 7}x²[/tex]
=(7)²
=49

88. [tex]\lim_{x \to -2}4x²-1[/tex]
=4(-2)²-1
=16-1
=15

89. [tex]\lim_{x \to 0} \frac{1}{1+sin(x)}[/tex]
=[tex]\frac{1}{1+sin(0)}[/tex]

=[tex]\frac{1}{1+0}[/tex]

=1

90. [tex]\lim_{x \to 2} e^{2x-x² }[/tex]
=[tex]e^{2(2)-2² }[/tex]
=[tex]e^{0 }[/tex]
=1

91. [tex]\lim_{x \to 1} \frac{2-7x}{x+6}[/tex]

=[tex]\frac{2-7(1)}{1+6}[/tex]

=[tex]\frac{-5}{7}[/tex]

92.[tex]\lim_{x \to 3}ln( e^{3x})[/tex]
=3x*ln(e)
=3(3)
=9