1. (a) Does the limit lim(r,y)→(1,1) ya² -y exist? x-1 (b) If the gradient of a function f(x, y) at the point (-1, –1) is given by Vf(-1, –1) = (2,3), then in what direction away from the point (-1,...

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Extracted text: 1. (a) Does the limit lim(r,y)→(1,1) ya² -y exist? x-1 (b) If the gradient of a function f(x, y) at the point (-1, –1) is given by Vf(-1, –1) = (2,3), then in what direction away from the point (-1, –1) does the function start to decrease fastest and what is the magnitude of the rate of change? (c) If the set DC R² is bounded and f(x, y) is continous on D, does f (x, y) have to acheive a maximum on D? (d) Let P = xy?, Q = x²y and C denote one petal of the four leaved rose defined by r = cost -<><. compute="" the="" line="" integral="" f.="" p="" dx="" +="" q="" dy.="" (20),="" (e)="" if="" s="" c="" r³="" is="" the="" unit="" sphere="" and="" f="STs" curl="" f="" n="" ds.="" (e"y,="" sin(22="" +="" y),="" xyz),="" then="" evaluate="" the="">