Let f:mathbb Ctomathbb C be a polynomial map. For R0, let gammaR:[0,1]tomathbb C be the map tmapsto Re^2pi it. Suppose that there exists cinmathbb R such that int0^1(fcircgammaR)(t),gammaR'(t),dtlongrightarrow cquadas Rlongrightarrowinfty. Which of the following statements is FALSE?

Q33Section B (Part B)33 of 120

Polynomial with a bounded contour-integral of modulus

Let $f:\mathbb C\to\mathbb C$ be a polynomial map. For $R>0$ , let $\gamma_R:[0,1]\to\mathbb C$ be the map $t\mapsto Re^{2\pi it}$ . Suppose that there exists $c\in\mathbb R$ such that

$\int_0^1\big|(f\circ\gamma_R)(t)\,\gamma_R'(t)\big|\,dt\longrightarrow c\quad\text{as }R\longrightarrow\infty.$

Which of the following statements is FALSE?

Pick an option to check your answer.

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