Zadanie 12f
Label the six roots counterclockwise, with z1 = 3 on the positive real axis. Find the total length of the five line segments joining z₁ to the other roots.
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Label the six roots counterclockwise, with z1 = 3 on the positive real axis. Find the total length of the five line segments joining z₁ to the other roots.
Sketch y=f(x), giving the equations of all asymptotes.
(i) Describe a sequence of transformations taking y=arctan x to y=f(x). (ii) State the inflection point.
(i) Find f⁻¹(x) and its domain. (ii) Find the intersection of y=f(x) and y=f⁻¹(x) with x>0.
Find the tangent equation at x=2.
The tangent referred to here is the tangent to y=f(x) at x=2. This tangent meets the curve again at a point P distinct from the tangency point. Find (i) P; (ii) the enclosed area.
Prove that dy/dx = −2e−2x(1 + y2).
Show that y″(0)=4.
Define for −0.2≤x≤0.2. Find its Maclaurin expansion through x².
Hence or otherwise evaluate .