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Derive the formula for differentiation from first principles

For a curve of f(x) against x, we can take the general point (x, f(x)) on the curve. By moving horizontally along the x-axis a distance of h, we also have the point (x+h, f(x+h)) on the curve. The gradient o...
NG
Answered by Nicola G. • Maths tutor
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Circle the number that is closest in value to (1.1)/(0.0204) [From selection of 5, 6, 50, 60] [Edit of 2018 Paper 1 Q4]

To simplify the question, the denominator can be rounded to 0.02 (to find an estimate), which comes out to be 1.1/0.02=55, which suggests that the answer is between 50 and 60, and not the other two.Now, an a...
DL
Answered by Doug L. • Maths tutor
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A sphere has a surface area of 4m^2, radius r. Another sphere has radius 2r. Calculate the Volume of the second sphere in M^3.

The surface area of a sphere can be calculated using Area = 4 x Pi x r^2. Since we know the surface are of the first sphere is 4m^2, we can write: 4 = 4 x Pi x r^2. This simplifies to r^2 = 0.318. Taking the...
FW
Answered by Freddie W. • Maths tutor
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If the base of an equilateral triangle is 3cm, and the height is 5cm, what is the area?

Area of a triangle = 1/2 x base x height 3 x 5 = 15cm1/2 of 15 = 7.5 Area = 7.5cm 2
Answered by • Maths tutor
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Find the two points of intersection of the graphs 2x+y=7 and x^2-8x+7=y. Solve using only algebraic methods (no graphical).

We treat this problem as two simultaneous equations, using our knowledge that when two graphs intersect, they simultaneously have the same solution. The second equation (quadratic equation) is already in the...
AS
Answered by Amy S. • Maths tutor
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