12. Find the area of the surface generated by rotating the curve y = √√x the y-axis. Do not integrate on your calculator from the point (0,0) to the point (1,1) around

Q: Sketch the graph of f(x,y) = 4x +y +1. State the domain and range of the function. Which of the…

A: f(x,y) = 4x2 + y2 + 1 Domain = R2 Range = [1, infinity)

Q: Parametrize the osculating circle to y = √x at x = 4.

A: Given that the osculating circle  y = x

Q: Find the points on the line 3x – 4y – 1 = 0 which are at a distance of 5 units from the point (3,…

A: Solving the problem by finding the points.

Q: Find the coordinates of the point/s on the curve y = 2x2 which are closest to the point ( 9, 0 ).

A:

Q: Find the area of the segment cut from the curve y=x (x-3) and the ordinates x=0 and x=5

A:

Q: Find the angle between the curve 2y=e-x/2 and y-axis

A: we will see in next step

Q: Find a point on the curve y = x2 that is closest to the point (18; 0)

A:

Q: Find the distance between the line x + y + 2 = 0 and the point (1, 1).

A: The distance between the line ax+by+c=0 and the point x1,y1 is given as below. d=ax1+by1+ca2+b2

Q: Find all smooth curves that intersect the curves x² = y +Cx at the right angle.

A: