Consider the function h(x)= (x^ 2 -1 )^ 1/3 + x

MATHEMATICS · Subjective · AP · Calculus AB · Limits and Continuity · Limits and Continuity

Problem

Consider the function h(x)=(x2−1)1/3+⌊x⌋,x∈R,h(x)=\bigl(x^{2}-1\bigr)^{1/3}+\lfloor x \rfloor , \qquad x\in\mathbb R, where ⌊x⌋\lfloor x \rfloor denotes the greatest–integer function. (i) Show that the term (x2−1)1/3\bigl(x^{2}-1\bigr)^{1/3} is continuous on R\mathbb R. (ii) Find all real numbers at which hh is not continuous. (iii) For each such number, classify the discontinuity and explain your answer. (iv) Hence write the maximal interval(s) on which hh is continuous.

Related theory

Browse the problem library