Given that \(y=\cos^{-1}x\), show that \((1-x^2)\dfrac{d^2y}{dx^2}-x\dfrac{dy}{dx}=0\).[2]
By differentiation of the result in part (a), find the first three non-zero terms of the Maclaurin expansion of \(\cos^{-1}x\). Give the coefficients in exact form.[3]
Using your answer to part (b), find the series expansion of \(e^{\cos^{-1}x}\) up to and including the term in \(x^3\). Give the coefficients in terms of \(e\).[3]
Solution:
Solution locked
Sign in to view the step-by-step solution
Similar questions are unavailable for this question.