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To solve this question, we need to use the chain rule, because the function is too complicated to solve simply by inspection. The chain rule says that dy/dx = dy/du × du/dx, where u is a function of x. In...

This question is asking to find the values for x, such that h(x) is strictly less than g(x). We can write this as 9^x + 9 < 103^x and solve for x as follows. 9^x + 9 < 103^x => 3^(2x) - ...

Straight away we notice that two trigonometric terms on the left hand side have 2x but there are no 2x on the right hand side therefore we realise that this question will require double angle formulae. If...

Consider the Left-Hand-Side (LHS) of the equation first. LHS: 1/2 + 1 + 2 + 2^2 + ... + 2^10. We identify this as a geometric series by noticing that dividing any term u_(n+1) by the preceding term n the ...

If you have an expression like 6x^2, to integrate it you have to add 1 to the power. Therefore, the new power will be 3. Then divide the whole expression by the new power so it will be 6x^3 divided by 3, ...