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1.3 Functions

1.3 Functions

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Question 62

A data engineer models the throughput T(x)T(x)T(x) of a high-frequency trading link, measured in terabits per millisecond, as a function of the signal frequency xxx in gigahertz:

T(x)=2x4−13x3+29x2−39x+41(x−3)2,x∈R,  x>3 T(x) = \frac{2x^4 - 13x^3 + 29x^2 - 39x + 41}{(x-3)^2}, \quad x \in \mathbb{R}, \; x > 3 T(x)=(x−3)22x4−13x3+29x2−39x+41​,x∈R,x>3
a.

Determine the values of the constants AAA, BBB, CCC and DDD such that

T(x)=Ax2+Bx+C+D(x−3)2 T(x) = Ax^2 + Bx + C + \frac{D}{(x-3)^2} T(x)=Ax2+Bx+C+(x−3)2D​
[4]
b.

Hence find

∫T(x) dx \int T(x) \, dx ∫T(x)dx
[3]
Markscheme

1.3 Functions Questions

  1. A Level
  2. /Maths
  3. /1.3 Functions

181 exam-style questions on OCR (MEI) A Level Maths 1.3 Functions, covering 1.3.1 Operations on polynomials, 1.3.2 Factor theorem, 1.3.3 Definition of a function (A-level only), 1.3.4 Composite functions (A-level only), 1.3.5 Inverse functions and their graphs (A-level only), 1.3.6 The modulus function (A-level only), 1.3.7 Inequalities with a modulus sign (A-level only), and 1.3.8 Functions in modelling (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.

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