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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,xR.

Show that f(x) has no vertical asymptotes.

[3]
a.

Find the equation of the horizontal asymptote. 

[2]
b.

Find the exact value of 10f(x)dx, giving the answer in the form lnq,qQ.

[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.

102x+6x2+6x+10dx=[ln(x2+6x+10)]10=ln17ln10=ln1710      M1A1A1

[3 marks]

c.

Examiners report

[N/A]
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b.
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c.

Syllabus sections

Topic 2—Functions » AHL 2.13—Rational functions
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Topic 2—Functions

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