Question

If `y` is a function of `x and log(x+y)-2xy=0` then the value of `y (0)` is equal to (a) `1` (b) `-1` (c) `2` (d) `0`
A. 1
B. -1
C. 2
D. 0

Answer 1

Correct Answer - A
When x=0, we have
`log(0+y)-2xx0xxy=0implieslogy=0impliesy=1`
Now, `log(x+y)-2xy=0`
Differentiating with respect to x, we get
`(1)/(x+y)(1+(dy)/(dx))-2y-2x(dy)/(dx)=0`
Putting x=0 and y=1, we get
`(1+(dy)/(dx))-2-2xx0=0implies(dy)/(dx)=1`