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Given h(x) = 9^x + 9 and g(x) = 10*3^x, find {x | h(x) < g(x)}.

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 &lt; 10 3^x and solve for x as follows. 9^x + 9 &lt; 10 3^x =&gt; 3^(2x) - 10 3^x + 9...
CM
Answered by Carlo M. • Maths tutor
4111 Views

Prove the following identity: (1+cos⁡(x)+cos⁡(2x))/(sin⁡(x)+sin⁡(2x) )=cot⁡(x)

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 yo...
JB
Answered by Jessica B. • Maths tutor
20022 Views

Given 1/2 + 1 + 2 + 2^2 + ... + 2^10 = a*2^b + c, find the values of a,b,c.

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 res...
CM
Answered by Carlo M. • Maths tutor
4280 Views

How do you do simple integration?

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, whi...
DS
Answered by Della S. • Maths tutor
3722 Views

Find the area under the curve of f(x)=4x/(x^2+1) form x = 0 to x = 2.

Solution of all integration problems starts with investigation of a given function. We can’t represent it with standard functions, i.e. linear, power or trigonometric. Second step would be to try substitutio...
ID
Answered by Igors D. • Maths tutor
6148 Views