Find the equations of the horizontal asymptotes

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Reference no: EM131127833

1)    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→5x2+1(2x+3)(x-5)=

2)    Evaluate the following limits. If needed, enter INF for ∞ and MINF for -∞.

lim x→∞ (1+2x)/(3-5x) =

lim x→-∞ (1+2x)/(3-5x) = 

3)    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) 

4)    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)= 

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))=

6)    Enter I for ∞, -I for -∞, and DNE if the limit does not exist.

limx→∞(√(4x^2+x)-2x)

Limit = 

7)    Enter I for ∞, -I for -∞, and DNE if the limit does not exist.

limx→∞(√(x^2+5)-√(x^2-10))

Limit =

1)    Note: Input inf for ∞∞, -inf for -∞-∞ or dne if needed.

limx→∞9cosx

Limit =

2)    Evaluate the following limits. If needed, enter 'INF' for ∞ and '-INF' for -∞.

limx→∞(-33x^2-15x^3)=

limx→-∞(-33x^2-15x^3)=

3)    Evaluate the following limit

limx→∞((9-√(x))/(9+√(x))

4)    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)=

5)    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=

6)    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))=       

Reference no: EM131127833

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