3.52: Derivative of $x\mathrm{sin}\,2x$ ; AP of twelve terms

0606/22/O/N/23 — Question 8 · 10 marks

(a)

A curve has equation

y=x\mathrm{sin}\,2x

. Find

\dfrac{\mathrm{d}y}{\mathrm{d}x}

[2]

(b)

Find the equation of the tangent to the curve at

x=\dfrac{\pi}{4}

[3]

(c)

Use your answer to part (a) to find the exact value of

\displaystyle\int_{0}^{\pi/6}2x\mathrm{cos}\,2x\,\mathrm{d}x

[5]

(a)

An AP has twelve terms. Sum of first three is

-36

; sum of last three is

72

. Find

a

and

d

[5]

3.52: Derivative of xsin 2xx\mathrm{sin}\,2xxsin2x; AP of twelve terms