If x is a prime number, then x+1 is not a prime number. A counterexample is x=
2 answers:
Answer: The required example is x = 5.
Step-by-step explanation: Given that if x is a prime nu mber, then x+1 is not a prime number.
We are to give a counterexample for this.
Let us consider that
Then, we know that x is a prime number.
But, we get
which is not a prime number.
Thus, the required example is x = 5.
You might be interested in
Answer:
1.8
Step-by-step explanation:
The point of intersection of the left-side function with the right-side function is the value of x where the two functions evaluate to the same quantity. That value of x is near 1.785, as indicated on the attached graph. Rounded to the nearest tenth, the value of x is 1.8.
_____
<em>Refinement of the graphical solution</em>
An iteration method called Newton's Method can be used to refine the estimate to the limit of accuracy of the calculator. For that, it is convenient to define a function such as the one you get when you subtract the right side from the left side. Newton's Method is good at finding the zero(s) of such a function.
The function defined as g(x) in the attachment is the iterator for Newton's Method. It gives the next "guess" based on the guess you give it as an argument. When there is no change, the guess is as accurate as the calculator can provide. Here, that refined estimate of x is x ≈ 1.78522264685.
