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Clash Royale CLAN TAG #URR8PPP up vote -1 down vote favorite Lets say there is car A which average speed is 20 m/s and is ahead of car b by 200 meters while car b average speed is 21 m/s and both are on a racing track that is 1700 meters in length. what is time gap between them? by time gap I mean by how many seconds. Notice their average speed isn't constant and can vary. How do I solve this and what formula should I use? calculus real-analysis physics share | cite | improve this question edited Aug 18 at 9:38 asked Aug 18 at 9:30 user7716943 1 1 Welcome to Mathematics Stack Exchange !! We are here to help you with any kind of mathematical problems, but you have to show what you have tried. :) – Anik Bhowmick Aug 18 at 9:35 You have to define "time gap" - there are two plausible meanings. – Craig Hicks Aug 18 at 9:35 @craig I mean like ho...

Clash Royale CLAN TAG #URR8PPP up vote 4 down vote favorite I want to find the asymptote oblique of the following function for $xrightarrowpminfty$ $$f(x)=sqrtx^2+3x=sqrtx^2left(1+frac3xx^2right)simsqrtx^2=|x|$$ For $xrightarrow+infty$ we have: $$fracf(x)xsimfracx=fracxx=1$$ which means that the function grows linearly. $$f(x)-mx=sqrtx^2+3x-x=xleft(sqrtfracx^2x^2+frac3xx^2-1right)sim xleft(frac 12cdotfrac3xright)=frac32$$ The oblique asymptote is $y=x+frac 3 2$ which is correct. For $xrightarrow-infty$ we have: $$fracf(x)x=fracx=frac-xx=-1$$ This means that $$f(x)-mx=sqrtx^2+3x+x=xleft(sqrtfracx^2x^2+frac3xx^2+1right)=xleft(sqrt1+frac3x+1right)sim xcdot2rightarrow -infty$$ Which is not what my textbook reports ($-frac32$). Any hints on what I did wrong to find the $q$ for $xrightarrow-infty$? limits asymptotics share | cite | improve this question asked Aug 18 at 9:13 Cesare 575 2 10 If $x < 0$ (or, better, $xleq -3$), one has $sqrtx^2...