Carefully explain, in a few sentences, why the equation square root of x=1+sinx ?
1 Answer
Feb 22, 2018
Here are some guesses as to what the question is. With answers.
Explanation:
Carefully explain, in a few sentences, why the equation
(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.