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How would I go about drawing the graph of f(x) = sin(x)/(e^x) for -π≤x≤2π?

Drawing this graph uses the same techniques as with most other functions. Just from inspection, we can see that as x increases, e^x also increases, and so the amplitude of the function will decrease (and ten...
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Answered by Jonah Z. • Maths tutor
6130 Views

2 log(x + a) = log(16a^6) where a is a positive constant. How do I find x in terms of a?

The left hand side of the equation can be rewritten as log(x+a)^2, using the power rule for logs. We can then simplify log(x+a)^2=log(16a^6) to (x+a)^2=16a^6. Taking the square root of both sides, we find x+...
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Answered by Emily V. • Maths tutor
15640 Views

How do I solve quadratic equation by completing the square : X^2 - 4X = 5

We have X 2 - 4X = 5, write the expression on the left side as X 2 - 2•2X = 5. Then we would need extra term 4 to complete the square, so adding 4 on the both sides gives us, X 2 - 2•2X + 4 = 5 +4. Simplify ...
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Answered by Rabin K. • Maths tutor
4393 Views

Integrate cos(4x)+16x^3 with respect to x

This is a simple integration, integrating each individual term with respect to x.For the cos(4x), you should use 'integration by substitution' as it is a function of a function.cos(4x) = cos(u) and u = 4x wh...
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Answered by Aadil C. • Maths tutor
4191 Views

When calculating a question with a double integral question between two different ranges which range relates to which integration variable.

When doing double integration with two arbitrary variables, for example 'x' and 'y' look at the Integration on the inside and integrate the function between the given range. For example if the integrand is t...
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Answered by Piranavan V. • Maths tutor
3625 Views