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Integration techniques — Question 282

Original QCE Vault practice · 5 marks

Q282 · Practice questionTechnology-freeComplex familiar5 marks

QUESTION 282 (5 marks)

A curve satisfies f′(x)=e−x/1−e−2xf\prime(x)=e^{-x}/\sqrt{1-e^{-2x}} for x>0x>0, and f(ln⁡2)=π/3f(\ln2)=\pi/3. Angles are in radians.
a)
Determine f(x) explicitly using a substitution.
[3 marks]
b)
Determine the limiting values as x→0+x\to0^+ and x→∞x\to\infty. Explain why x=0 is outside the derivative domain.
[2 marks]
Question linkSyllabus coverage

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