11.1 Integrating Standard Functions
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The curve C has equation y=f(x)y = \text{f}(x)y=f(x) where x>0x > 0x>0.

Given that

  • f′(x)=(x+2)2xx\text{f}'(x) = \dfrac{(x + 2)^2}{x\sqrt{x}}f′(x)=xx​(x+2)2​
  • the point P(9,30)P(9, 30)P(9,30) lies on C
a.

(i) Find the value of the gradient of the curve at PPP.

(ii) Hence find the equation of the tangent to CCC at PPP, giving your answer in the form ax+by+c=0ax + by + c = 0ax+by+c=0, where aaa, bbb and ccc are integers to be found.

[4]
b.

Find f(x)\text{f}(x)f(x), simplifying your answer.

[6]

11.1 Integrating Standard Functions Questions

Practise Edexcel A Level Maths 11.1 Integrating Standard Functions with exam-style questions for A Level Maths. 81 questions, matched to the Edexcel A Level Maths (9MA0) specification and written in Paper 1, Paper 2 and Paper 3 style. Every question includes a full worked solution and mark scheme, so you can see where marks are awarded rather than just whether you got the answer right.

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11.1 Integrating Standard Functions Questions

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