Question

how do you find the horizontal and vertical assymptotes of the curve
y= x/ x+3 and also the intercepts.

so that you can approximate the area under the curve from x=1 to x=5 using 5 function values?

THANKYOU,

Answer 1

There is a vertical asymptote at x = -3 and a horizontal asymptote of y = 1, as x approaches + or = infinity.
The x-intercept is where x = 0, which would be y = (0,0). The y intercept would be where y = 0, or (also) (0,0). There is ony one intercept.

To approximate the area uner the curve, use the trapezoidal or Simpson's rule. and computed values of f(x) at x = 1,2,3,4 and 5. These values are 1/4, 2/5, 1/2, 4/7 and 5/8.

Answer 2

What happens to the function as x>>-3 ?

What happens to the function as x>>inf
What happens to the function as x>>-inf

appx area. I am not certain of the technique you have been taught.