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The area of a circle is given by (pi)r² and the area generated by R can be considered as an infinite number of circular areas.

Thus, we can write the area gene...

Having two real roots is equivalent to having two intersections with the x axis.

The equation is a parabola (a U shape) so, having two real roots is equivalent to having the lowest point ...

1. Set y=a^x2. Take the natural log of both sides: ln(y)=ln(a^x)3. Using the log rules, simplify: ln(y)=xln(a)4. Differentiate both sides with respect to x: 1/y dy/dx=lna+05. Rearrange: dy/dx=yln(a)6. ...

1. Differentiate the Equation of the curve to find the gradient: y'=3x^2

2. The gradient of the tangent is found by substituting x=1 into y'=3x^2: Gradient of tangent=3

3. N...

We are given the substitution to use, so the first step is to differentiate "u" with respect to x. 

du/dx = -sin(x)

Now, to replace the "dx&q...