# Answer in Calculus for bri #260974

(3) (i) A broken pipe at an oil rig off the east coast of Trinidad produces a circular oil slick that is S meters thick at a distance x meters from the break. It difficult to measure the thickness of the slick directly at the source owing to excess turbulence, but for x >0 they know that s(x) = x^2/2 + 5/3x/x^3 + x^2 + 2x If the oil slick is assumed to be continuously distributed, how thick is expected to be at the source? (ii) If f(x) = {4x + 7 1< x < 2, 4x^2 – 1 2< x < 4 , determine whether the function f (x) is continuous throughout its domain?

I.

“limlimits_{xto0} space frac{frac{x^2}{2}+frac{5}{3}x}{x^3+x^2+2x}\nnlimlimits_{xto0} space frac{X(frac{x}{2}+frac{5}{3})}{X(x^2+x+2}\nnlimlimits_{xto0} space frac{frac{x}{2}+frac{5}{3}}{x^2+x+2}”

“frac{frac{x}{2}+frac{5}{3}}{0^2+0+2}=frac{5}{6}”

Oil slick is “frac{5}{6}”m thick of source.

ii.

“f(x)=begin{bmatrix}n 4x+7 & 1nu2264nxnnnu22642\n 4x^2-1& 2<xu22644nend{bmatrix}”

“limlimits_{xto2^-}(4x+7)\=4(2)+7\=13”

“limlimits_{xto2^+}(4x^2-1)\=4(2)^2-1\=15”

“limlimits_{xto2^-} f(x)neq limlimits_{xto2^+} f(x)”

f(x) is discontinuous at x=2.