A curve has the equation (5-4x)/(1+x)
Start by looking for intercepts.x=0, y= 5. Therefore the curve crosses the y axis at y=5y=0, x= 5/4these are the only two intercepts. Now look for asymptotes.3. at x= 1, y becomes undefined, looking at either side of x= 1. As x tends towards 1 from the positive direction y tends towards positive infinity. As x tends towards 1 from the negative direction, y tends towards negative infinity.4. As x tends towards infinity we can split out the equation. y= 5/(1+x) - 4x/(1+x). As x grows larger, y 5/(1+) becomes smaller, and -4x/(1+x) tends towards -4x/x = -4. Therefore as x tends towards infinity, y tends towards -4. Together this permits us to draw out the sketch of the equation.
HH
Answered by Henry H. • Further Mathematics tutor
2655 Views
See similar Further Mathematics A Level tutorsRelated Further Mathematics A Level answers
All answers ▸Integrate cos(log(x)) dx
a) Show that d/dx(arcsin x) = 1/(√ (1-x²)). b) Hence, use a suitable trigonometric substitution to find ∫ (1/(√ (4-2x-x²))) dx.
Using mathematical induction, prove that n^3+2n is divisible by 3 for all integers n
Differentiate arcsin(2x) using the fact that 2x=sin(y)