Edexcel A Level Further Maths
Topic questions Pure mathematics Differentiating hyperbolic functions
7 questions · 55 marks · about 1 hour
Given that
show that
where k is a constant to be determined.
Hence determine the first three non-zero terms of the Maclaurin series for y, giving each coefficient in simplest form.
4 sinhx = pcoshxwhere p is a real constant
Given that this equation has real solutions, determine the range of possible values for p
y = coshn x n 
5
Show that
Hence determine the first three non‑zero terms of the Maclaurin series for y, giving each coefficient in simplest form.
y = coshn x n 5
Show that
Hence determine the first three non‑zero terms of the Maclaurin series for y, giving each coefficient in simplest form.
Use a hyperbolic substitution and calculus to show that
where k is an arbitrary constant.
Figure 1 shows a sketch of part of the curve C with equation
The finite region R, shown shaded in Figure 1, is bounded by the curve C, the x‑axis and the line with equation x = 3
Using algebraic integration and the result from part (a), show that the area of R is given by
The curve C has equation
Determine, in terms of natural logarithms, the exact x coordinates of the stationary points of C.
The curve C has equation
Determine, in terms of natural logarithms, the exact x coordinates of the stationary points of C.
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