Explain please Consider the following piecewise-defined function. where k R. How

Question

Explain please

Consider the following piecewise-defined function. where k R. How should we choose the value of k so that f is continuous at x = 4? Discuss how the continuity (at a point, say x = c) and the existence of the limit of a function (as x rightarrow c) relate. Does one imply the other? That is, does the continuity of a function at x = c imply the existence of the limit as x rightarrow c? What about the converse? Which condition is stronger/weaker? For the weaker implication, provide a counterexample to justify vour claim.

Explanation / Answer

the function is called continuous if it has same value at the breaking point.

here at 4- the value is undefinded so we get limiting or approching value at 4- ,so differentiating wrt to x(l'hosp rule) we get :

2x/2x-1 , now if x =4 ,f(x) = 8/7 = k

Related Questions

Navigate

• Browse (All)
• Browse E
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.