Find horizontal and vertical asymptotes for y=(1)/((x+2)^3)

Vertical asymptote:

Horizontal asymptote: or x axis.

Step-by-step explanation:

The rational function is given as:

Vertical asymptotes are those values of for which the function is undefined or the graph moves towards infinity.

For a rational function, the vertical asymptotes can be determined by equating the denominator equal to zero and finding the values of .

Here, the denominator is

Setting the denominator equal to zero, we get

Therefore, the vertical asymptote occur at .

Horizontal asymptotes are the horizontal lines when tends towards infinity.

For a rational function, if the degree of numerator is less than that of the denominator, then the horizontal asymptote is given as .

Here, there is no term in the numerator. So, degree is 0. The degree of the denominator is 3. So, the degree of numerator is less than that of denominator.

Therefore, the horizontal asymptote is at or x axis.

the value of v.w= -12.

step-by-step explanation:

we are given three vector r,v and w as:

r = < 5, -5, -2> ; v = < 2, -8, -8> ; w = < -2, 6, -5>

we know that r,v and w could also be represented as:

r=5i-5j-2k

v=2i-8j-8k

and w= -2i+6j-5k

where i,j and k are the unit vectors of x,y and z-axis respectively.

also we know that it has the following property:

i.i=1 ; j.j=1; k.k=1

and i.=j.i=i.k=k.i=j.k=k.j=0

i.e. when we multiply two vectors or we find it's dot product we need to only multiply the components of x coordinates with each other; y with each other and z with each other.

hence, v.w= (2i-8j- -2i+6j-5k)

                  = 2×(-2)+(-8)×(6)+(-8)×(-5)

                  = -4-48+40

                  = -12

hence, v.w= -12