Question

(d) Which picture shows the curve C? Recall the curve C is defined by x f(t) cost t yg(t) sint - t 2아 2아 10 10 0 0 -10 -10 -2아 -20 20 10 20 -20 10 -20 -10 0 -10 (i) (ii) X X 2아 20 1아 1아 아 0 -10 -10 -20 -2아 10 20 -20 -10 10 20 -20 -10 0 0 (iv) (iii) X X (e) Find an equation for the tangent line at the point tT Consider the curve C defined by the parametric equations: f(t) COstt sin t t (a) Find the limit of y/x as t to0. (b) At what (r, y) point(s) does the curve C have vertical tangent (s)? (c) Determine the t-values or t-range for which the concavity of the curve is zero

Answer 1

20 10- -20 10 -10 20 0 -10 -20

From the above figure, the option (IV) is correct.

Equahen angemta (e) Sun)t (x2 - T asaltd? (riXP dt intti Nou dt T- X - &int The en tangent 222 t 2T y+2X -2.t-71

Lismit a t + o lim in GAtt 2 nt Lim bdta Si nt _int Sindd im i Nou GAt t9.ob -

dF Veatical ungent Sint int 4