Ques 3 fast pleadse 1.(x, y) = (0,0)Discuss the continuity of f(x,y). And show that f,(x, y) and f,(x,y) exist at allpoints (x, y).6. Find the equation of parabola which has axis parallel to...

Ques 3 fast pleadse


Extracted text: discuss its concavity. Also, sketch the curve. 2. Evaluate the following limits using L'Hopital's rule and lim,x- In(x5 – 1010)]. limxb x*ーb5 3. Find the volume of the solid obtained by revolving the region bounded by the curves y = 2x2 + 1 and y = 3 - 2x2 about x-axis. Also find the length of the plane curve y = 2x2 + 1 over the interval [1, 3] 4. Sketch the graph of r² = 0²,0 < 0="" in="" polar="" coordinates.="" xyn="" (x,="" y)="" +="" (0,0)="" 5.="" let="" f(x,="" y)="x*+y3n!" 0,="" where="" n=""> 1. (x, y) = (0,0) Discuss the continuity of f(x,y). And show that f,(x, y) and f,(x,y) exist at all points (x, y). 6. Find the equation of parabola which has axis parallel to y-axis and which passes through the points (0, 2), (–1,0) and (1, 6). And plot this parabola. An ellipse circumscribes a rectangle whose sides are given by x = +2 and y = +4. If the distance between the foci is 4V6 and major axis is along y-axis, then find the equation of the ellipse. Also, plot this ellipse. %3D