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f(x) = 2x^3 – 7x^2 + 4x + 4 (a) Use the factor theorem to show that (x – 2) is a factor of f(x). (2) (b) Factorise f(x) completely.

We are presented with a third order polynomial with 4 terms, so we expect 3 solutions for f(x)=0. To prove that (x-2) is a factor we must insert the value of x=2 into the function and if f(2)=0 then we have ...
NA
Answered by Nazar A. • Maths tutor
16239 Views

Consider a cone of vertical height H (in metres) and base radius R (in metres) which is full with water. The cone, at time t=0, starts to leak such that it loses water at a rate of k m^3 per second. Give an expression for the rate of change of H.

L = (H 2 +R 2 ) 1/2 V = (1/3)πR 2 (H 2 +R 2 ) 1/2 dV/dt = -k dH/dt = dH/dV × dv/dt dV/dH = (1/3)πR 2 H(H 2 +R 2 ) 1/2 Thus, dH/dt = -3k/(πR 2 H(H 2 +R 2 ) 1/2 ) ​​​​​ ​​​​ ​​
CE
Answered by Callum E. • Maths tutor
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Integrate the following function: f(x) = ln(x)

∫ln(x)dx = xln(x) - ∫x/x dx = xln(x) - x + C
CE
Answered by Callum E. • Maths tutor
3763 Views

Why is the differential of a constant zero?

Any constant (say k) can be rewritten as kx 0 since x 0 =1. When you differentiate this, the 0 which is the power of the x term gets dragged to the front and is multiplied with the rest of the expression (ac...
JC
Answered by Jawad C. • Maths tutor
4221 Views

How do you find the maximum/minimum value of an equation?

When finding the maximum or minimum of an equation, make sure you rearrange an equation to make y the subject of the equation i.e. y=_________. You can then differentiate with respect to x and then set the d...
JC
Answered by Jawad C. • Maths tutor
7453 Views