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Degree: MSc Mathematics and Foundations of Computer Science (Masters) - Oxford, Oriel College University

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Have memorised all the digits of Pi, but still working on their order.

Currently enrolled on an MSc in Mathematics and Foundations of Computer Science at Oxford University.

The focus of my lessons will be on providing you with the tools to independently work through problems.

Subjects offered

SubjectQualificationPrices
Further Mathematics A Level £20 /hr
Maths A Level £20 /hr
Maths GCSE £18 /hr
Maths IB £20 /hr
Maths 13 Plus £18 /hr
Maths 11 Plus £18 /hr

Qualifications

MathematisDegree (Bachelors)1ST
 CRB/DBS Standard No CRB/DBS Enhanced No

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What's the integral of x^2 +3/x, with respect to x?

A: x3/3 + 3ln(x) + A. Step-by-step solution: Integral (x2+3/x dx) = [as integrals preserve sums] integral (x2 dx) + integral (3/x dx) = [raise exponent by one, multiply by the reciprocal, add a constant] x3/3 + C + integral (3/x dx) = [3 is a constant, so we we can take it out of the integ...

A: x3/3 + 3ln(x) + A.

Step-by-step solution:

Integral (x2+3/x dx) =

[as integrals preserve sums]

integral (x2 dx) + integral (3/x dx) =

[raise exponent by one, multiply by the reciprocal, add a constant]

x3/3 + C + integral (3/x dx) =

[3 is a constant, so we we can take it out of the integral. The anti-derivative of 1/x dx is ln(x)+D, which is a standard result you need to know]

x3/3 + C + 3(ln(x) + D)=

[merge the constants into one constant]

x3/3 + 3ln(x) + A.

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2 years ago

710 views

What's the inverse of the function f=x+2?

If we apply a function and then its inverse, we should get back to where we started.  Suppose we start with an element x. If we apply f to it, we get to x+2. In order to get back to where we started (i.e. x), we need to subtract 2. Hence, the inverse of the function f is f-1=x-2.

If we apply a function and then its inverse, we should get back to where we started.

Suppose we start with an element x. If we apply f to it, we get to x+2. In order to get back to where we started (i.e. x), we need to subtract 2.

Hence, the inverse of the function f is

f-1=x-2.

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2 years ago

727 views
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