1. Limits and Continuity

Analyze lim x→∞ f(x) and lim x→−∞ f(x), and then identify any horizontal asymptotes.

f(x) = (√(16x⁴ + 64x²) + x²) / (2x² − 4) 

Analyze lim x→∞ f(x) and lim x→−∞ f(x), and then identify any horizontal asymptotes.

f(x) = (3x⁴ + 3x³ − 36x²) / (x⁴ − 25x² + 144)

Find the vertical asymptotes. For each vertical asymptote x = a, analyze lim x→a^- f(x) and lim x→a⁺ f(x).

f(x) = (3x⁴ + 3x³ − 36x²) / (x⁴ − 25x² + 144)

Find the vertical asymptotes. For each vertical asymptote x = a, analyze lim x→a^- f(x) and lim x→a⁺ f(x).

f(x) = x²(4x² − √(16x⁴ + 1))

Analyze lim x→∞ f(x) and lim x→−∞ f(x), and then identify any horizontal asymptotes.

f(x) = (x² − 9)/(x(x−3))

Analyze lim x→∞ f(x) and lim x→−∞ f(x), and then identify any horizontal asymptotes.

f(x) = (x⁴ − 1)/(x^2−1)

Find the vertical asymptotes. For each vertical asymptote x=a, analyze lim x→a^- f(x) and lim x→a⁺ f(x).

f(x) = (x^4−1)/(x^2−1)

Analyze lim x→∞ f(x) and lim x→−∞ f(x), and then identify any horizontal asymptotes.

f(x)=√x^2+2x+6−3 / x−1

Find the vertical asymptotes. For each vertical asymptote x=a, analyze lim x→a^− f(x) and lim x→a^+f(x).

f(x)=√x^2+2x+6−3 / x−1

Analyze lim x→∞ f(x) and lim x→−∞ f(x), and then identify any horizontal asymptotes.

f(x)=|1−x^2| / x(x+1)

Find the vertical asymptotes. For each vertical asymptote x=a, analyze lim x→a^− f(x) and lim x→a^+f(x).

f(x)=|1−x^2| / x(x+1)

Analyze lim x→∞ f(x) and lim x→−∞ f(x), and then identify any horizontal asymptotes.

f(x)=3e^x+10 / e^x

Find the vertical asymptotes. For each vertical asymptote x=a, analyze lim x→a^− f(x) and lim x→a^+f(x).

f(x)=3e^x+10 / e^x

Analyze lim x→∞ f(x) and lim x→−∞ f(x), and then identify any horizontal asymptotes.

f(x)=cos x+2√x / √x.

Find the vertical asymptotes. For each vertical asymptote x=a, analyze lim x→a^− f(x) and lim x→a^+f(x).

f(x)=cos x+2√x / √x.