Taeyeon

Consider the curve defined by 2y^3+6X^2(y)- 12x^2 +6y=1 . a. Show that dy/dx= (4x-2xy)/(x^2+y^2+1) b. Write an equation of each horizontal tangent line to the curve. c. The line through the origin with slope -1 is tangent to the curve at point P. Find the...

5. A particle moves along the y – axis with velocity given by v(t)=tsine(t^2) for t>=0 . a. In which direction (up or down) is the particle moving at time t = 1.5? Why? b. Find the acceleration of the particle at time t= 1.5. Is the velocity of the partic...

1. If 3x^2+2xy+y2=2 then the value of dy/dx x = 1 is A. -2 B. 0 C. 2 D. 4 E. not defined

3. For what value of k will x+k/x have a relative maximum at x = -2? A. -4 B. -2 C. 2 D. 4 E. None of these

1. Let R be the region in the first quadrant enclosed by the graphs of y=4-X , y=3x , and the y-axis. a. Find the area of region R. b. Find the volume of the solid formed by revolving the region R about the x-axis.

2. Let R be the region of the first quadrant bounded by the x-axis and the cuve y=2X-X^2 a. Find the volume produced when R is revolved around the x-axis b. Find the volume produced when R is revolved around the y-axis

A piece of wooden rod 31 cm long is to be cut into three parts, two of which are to be of equal length. the length of each of the two equal part is 5 cm longer than third part. find their lengths. solution pls.

This is what I found in the paper though.