Sketch the graph of \(y=\dfrac{3x^2+4x+5}{x^2+8x+15}\). Label clearly the equations of the asymptotes of the graph and the coordinates of the turning points and the point(s) where the graph cuts the axes.[7]
Hence solve the inequality \(\dfrac{-2x^2+4x+10}{x^2+8x+15}\leq\mathrm e^{-x}\).[5]
Solution:
Solution locked
Sign in to view the step-by-step solution
Similar questions are unavailable for this question.
Answer:(a) Asymptotes \(x=-5,-3\), \(y=3\); maximum \((-3.73,-34.3)\), minimum \((-0.268,0.321)\), intercept \((0,\dfrac13)\). (b) \(x<-5\), \(-4.72\leq x\leq-3.59\), \(-3<x\leq0.522\), or \(x\geq3.23\).