Give a counterexample to the statement “If n is an integer and n2 is divisible by 4, then n is divisible by 4.” To give a counterexample, I have to find an integer n such n2 is divisible by 4, …

For instance, a polynomial as an example of a continuous function is not a counterexample, but a polynomial as an example of a function that fails to be bounded or of a function that fails to be …

To make it valid, we’ll need to ADD a claim about the relationship between being a mammal and having hair. Something like: All dolphins are mammals. All mammals are things that have hair. …

Counterexample The function y 3p D x2 is continuous on R and the tangent line exists at any point on its graph, but the function is not differen-tiable at the point x D 0.

We suggest the following counterexample: In order to see that these two linear functions are not perpendicular, we notice that the slop of the rst function is 3. Therefore, the slope of a …

Oct 26, 2012 · In this between, there are examples that we call them counterexamples, that with their help we receive deeper conceptual understanding and enhance critical thinking skills.

Counterexample without cases J. Marshall Ash Abstract. The standard examples of functions without a one-sided limit are defined piecewise, with at least two pieces. We give an example …