Find the general solution: 3x/2 = dx/dy
First separate the variables: 3x dx = 2 dy Then integrate both sides of the equation: 3x^2+C=2y Where C is a constant. So the general solution is 3/2 x^2 + 1/2C = y but since C is an unknown constant, the 1/2 coefficient is unnecessary, The solution is 3/2 x^2 + C = y.
What is the limit as x approaches infinity of 1/x?
As x grows without bound towards positive infinity, the fraction 1/x gets smaller. Example: 1/2 > 1/4 > 1/8 However, the fraction never becomes negative, so it approaches zero. Therefore, the limit as x approaches infinity of 1/x is 0.
Solve for x: 4x^2 + 4x + 1 = 0
4x^2 + 4x + 1 = 0 (2x+1)(2x+1)=0 2x+1=0 2x=-1 x=-1/2