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This is a typical AS-level Maths question.
We see it’s a definite integral so start by drawing some big square brackets with the “limits” (2 and 1).
We go through the ex...
To sketch a graph of an equation, there are several key features to consider. Firstly, we can consider where the graph crosses the x- and y-axes. When x=0, y=0, so the graph goes through the origin. If y=...
You can split the derivative into 2 parts: dx/dy (x^2*e^x) + dx/dy (x)
For the first part you have to use the product rule, so let U=x^2 V=e^x U'=2x V'=Chain rule
V'=dx/dy(e^x)dx/dy(x)...
The first thing we want to do is re-write the curve f(x) in a format in which we can read and easily plot a graph. If we can include the '3x' in the factorised part of the equation, it will be neater and ...
In order to find the gradient of the curve at (1,1), we must first differentiate the equation of the curve. To do this, multiply the coefficient of x by the power of that same x. Then subtract one from th...
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