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Integrate a^x with respect to x

This comes up in C4 in A level maths and differentiating it could come up in C3. You can write a^x as exp(ln(a^x))=exp(xln(a)) then differentiating this, you get ln(a)exp(xln(a))=ln(a)a^x. By differen...

JW
Answered by John W. Maths tutor
40533 Views

Give an example of a negative feedback mechanism in the human body.

When the hypothalamus in the brain detects that the blood is getting too concentrated (not enough water), it stimulates the pituitary gland to release an anti-diuretic hormone (ADH). When it reaches the k...

PM
Answered by Paul M. Biology tutor
7782 Views

How do current and voltage vary in series and parallel circuits, respectively?

In a series circuit, the current is the same throughout; the voltage is split among the components (such as LEDs or resistors) in proportion to the resistance of the components (higher resistance means mo...

PM
Answered by Paul M. Physics tutor
14667 Views

What is the function of a catalyst in a chemical reaction?

It provides an alternative reaction pathway with a lower activation energy. However, it does not lower the activation energy for the 'normal' reaction without a catalyst.

PM
Answered by Paul M. Chemistry tutor
19377 Views

Prove that √2 is irrational

Prove by contradiction: Assume negation to be true i.e. √2 is rational Then √2 can be written in the form a/b where a and b are integers with no common factor (the fraction cannot be simplified) => a/b...

PM
Answered by Paul M. Maths tutor
8096 Views

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