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(a) The curve is defined by y=(2x-3)^5. To find x=w when y=-32, we must substitute these values into the equation C and re-arrange to find w. -32=(2w-3)^5. First we must remove the power of 5 by doing pow...
The equation of a straight line is usually given in the form y = mx + c. To prove that two lines are parallel we will need to show that both lines have the same gradient. The gradient of a line is the slo...
This is a standard question that may be found in a C4 mathematics paper. Students should use knowledge of the volume of revolution formula V = piint_{a}^{b} y2dx to find the expression V =...
Proof by induction is a powerful proof technique that can be used to prove a certain property and is a common question on the IB exams. Consider for instance the problem "Prove that sinx + sin3x +......
To begin, we must first use the fact that turning points of a graph occur at points where the gradient is equal to zero, in other words, points where dy/dx =0. Differentiating the equation with and settin...
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