Date | May Example questions | Marks available | 3 | Reference code | EXM.1.AHL.TZ0.4 |
Level | Additional Higher Level | Paper | Paper 1 (without calculator) | Time zone | Time zone 0 |
Command term | Find | Question number | 4 | Adapted from | N/A |
Question
Let f(x)=2x+6x2+6x+10,x∈R.
Show that f(x) has no vertical asymptotes.
[3]
a.
Find the equation of the horizontal asymptote.
[2]
b.
Find the exact value of 1∫0f(x)dx, giving the answer in the form lnq,q∈Q.
[3]
c.
Markscheme
x2+6x+10=x2+6x+9+1=(x+3)2+1 M1A1
So the denominator is never zero and thus there are no vertical asymptotes. (or use of discriminant is negative) R1
[3 marks]
a.
x→±∞,f(x)→0 so the equation of the horizontal asymptote is y=0 M1A1
[2 marks]
b.
1∫02x+6x2+6x+10dx=[ln(x2+6x+10)]10=ln17−ln10=ln1710 M1A1A1
[3 marks]
c.
Examiners report
[N/A]
a.
[N/A]
b.
[N/A]
c.