Find the two x values at which the tangent line to the curve y=(x + 3)/(x + 2) is perpendicular to the line y = x.

1). To be perpendicular to y=x which has a slope of 1 the tangent of the curve must have a slope of -1

dy/dx=(x+2-x-3)/(x+2)^2

dy/dx=-1/(x+2)^2

dy/dx must equal -1 to be perpendicular to y=x

-1/(x+2)^2=-1

-1/(x^2+4x+4)=-1

-1=-x^2-4x-4

x^2+4x+3=0

x^2+x+3x+3=0

x(x+1)+3(x+1)=0

(x+3)(x+1)=0

x=(-1, -3)

2). y = x + 3/x + 2

Plots: x from - to - 1.6

Plot: x from - 6 to 1.4

Alternate Form: 

y = 1/x + 2  + 1

(x + 2) y = x + 3

Expanded form:

y = x/x + 2 + 3/x + 2

Root: x = - 3

Limit:

3 + x/2 + x = 1

answer: a. 13/44

step-by-step explanation: judging by the information given to us, we are looking for experimental probability. we can see that 13 males have chosen chocolate ice cream. there are 44 ice creams in total (remember that the total is always the denominator). so our answer is 13/44.

your question is incomplete, write all the numbers in the sequence that it tells you.  

step-by-step explanation: