Marco G.

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

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3 completed lessons

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.

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.

#### Personally interviewed by MyTutor

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#### Qualifications

MathematisDegree (Bachelors)1ST

#### General Availability

Pre 12pm12-5pmAfter 5pm
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#### Subjects offered

SubjectQualificationPrices
Further MathematicsA Level£20 /hr
MathsA Level£20 /hr
MathsGCSE£18 /hr
MathsIB£20 /hr
Maths13 Plus£18 /hr
Maths11 Plus£18 /hr

### 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 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.

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.

2 years ago

871 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.

2 years ago

881 views

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