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A function is said to have a vertical asymptote wherever the limit on the left or right (or both) is either positive or negative infinity. For example, the function f(x)=(x^2+1)/((2x+3)(x−5)) has a vertical asymptote at x=5

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  • A function is said to have a vertical asymptote wherever the limit on the left or right (or both) is either positive or negative infinity. For example, the function f(x)=(x^2+1)/((2x+3)(x−5))   has a vertical asymptote at x=5

For each of the following limits, enter either ‘P’ for positive infinity, ‘N’ for negative infinity, or ‘D’ when the limit simply does not exist.
lim x→5 −  x 2 +1(2x+3)(x−5) = limx→5−x2+1(2x+3)(x−5)=

lim x→5 +  x 2 +1(2x+3)(x−5) = limx→5+x2+1(2x+3)(x−5)=

lim x→5    x 2 +1(2x+3)(x−5) = limx→5×2+1(2x+3)(x−5)=

 

  • Evaluate the following limits. If needed, enter INF for ∞ and MINF for −∞.

lim x→∞ (1+2x)/(3−5x) =

lim x→−∞ (1+2x)/(3−5x) =

  • Evaluate the following limits. If needed, enter INF for ∞ and MINF for −∞.

lim x→∞ (8x^3−6x^2)/(−9x10−2x−5x^3)

lim x→−∞ (8x^3−6x^2)/(−9x10−2x−5x^3)

  • Evaluate the following limits. If needed, enter INF for ∞ and MINF for −∞.

lim x→∞ (7x+88x^2)/(−5x+5)=

lim x→−∞ (7x+88x^2)/(−5x+5)=

  • Evaluate the following limits. If needed, enter INF for ∞ and MINF for −∞.

limx→∞(√(3+3x^2))/(2+5x))=

limx→−∞(√(3+3x^2))/(2+5x))=

  • Enter I for ∞, -I for −∞, and DNE if the limit does not exist.

limx→∞(√(4x^2+x)−2x)

Limit =

  • Enter I for ∞, -I for −∞, and DNE if the limit does not exist.

limx→∞(√(x^2+5)- √(x^2−10))

Limit =

  • Note: Input inf for ∞∞, -inf for −∞−∞ or dne if needed.

limx→∞9cosx

Limit =

  • Evaluate the following limits. If needed, enter ‘INF’ for ∞ and ‘-INF’ for −∞.

limx→∞(−33x^2−15x^3)=

limx→−∞(−33x^2−15x^3)=

  • Evaluate the following limit

limx→∞((9−√(x))/( 9+√(x))

  • Evaluate the following limits. If needed, enter inf for ∞ and -inf −∞.

limx→∞x^2(−2+9x)(−9−3x)=

limx→−∞x^2(−2+9x)(−9−3x)=

  • Find the equations of the horizontal asymptotes and the vertical asymptotes of f(x)f(x). If there are no asymptotes of a given type, enter NONE. If there is more than one asymptote of a given type, give a comma separated list (i.e.: 1, 2,…).

f(x)=((x^2+x−6)/(3x^2+7x−6))

Horizontal asymptotes: y=

Vertical Asymptotes: x=

  • Evaluate the following limits, use “infinity” for “∞” and “-infinity” for “−∞”.

limx→5−((2)/(x−5)^3)) =

limx→3+((2)/(x−3))=

limx→3−((2)/(x−3))=

limx→−7−((1)/(x^2(x+7))=