Question

Carefully explain, in a few sentences, why the equation square root of x=1+sinx ?

Answer 1

Here are some guesses as to what the question is. With answers.

Explanation:

Carefully explain, in a few sentences, why the equation `sqrtx=1+sinx`,

(a) is not an identity.

Because for some values of `x`, it is not true. For example: `sqrt(0) != 1+sin(0)`

(b) has a solution

Because `f(x) = 1+sinx-sqrtx` is continuous on `[0,pi]` and `0` is between `f(0) = 1` and `f(pi) = 1-sqrtpi`. So the intermediate Value Theorem assures us that there is a `c` in `(0,pi)` with `f(c) = 0`. This `c` solves the equation.

(c) does not have two distinct solutions.

I cannot answer this (except to look at the graph.)

If I think of more guesses about what the question is, I'll post them and answer them.