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Let g(x)=ekx, where −1<k<1.
Write down an expression for
g′(x)
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g′′(x)
Let g(n) denote the nth derivative of g.
Write down an expression for g(n)(x).
The function f is defined by f(x)=g(x)+g′(x)+g′′(x)+g(3)(x)+g(4)(x)⋯
Show that f(x)=1−kekx.
The line L is tangent to curve y=f(x) at point (p,2), and intercepts the x-axis at p−4.
Find the value of p giving your answer in the form ln(n)−ln(m), where n,m∈Z.
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