*Identify the location of any discontinuities of f (x) attached *For each discontinuity, determine the type of discontinuity by evaluating the left- and right-side limits. f(x)=x−1x2+x

Question

*Identify the location of any discontinuities of f (x) attached  *For each discontinuity, determine the type of discontinuity by evaluating the left- and right-side limits.  f(x)=x−1x2+x

saiyansruleA · Accepted Answer

To determine the nature of discontinuities of the given function.  The function is not defined at the points x=0 and -1 ; (at all other points , it is continuous). The points of discontinuities are x=0 and x=-1  f(x)=x−1x2+x  =x−1x(x+1)(x≠0,−1)  Analyzing the left and right hand limits at x=0   Left hand limit  =limx→0−f(x)=limx→0−(1x)×limx→0x−1x+1=∞  Right - hand limit  limx→0−=limx→0−(1x)×limx→0x−1x+1=−∞  (∴limx→0x−1x+1=−1)  Nether limits exist, so f(x) has discontinuity of the second kind at x=0  Analyzing the discontinuity at x=-1  Left - hand limit  =limx→−1−f(x)=limx→−1−(1x+1)×limx→−1x−1x=−∞  Right - hand limit  limx→−1+=limx→−1+(1x+1)×limx→−1x−1x=∞  (∴limx→−1x−1x=2)  Nether limits exist, so f(x) has discontinuity of the second kind at x=-1  ANSWER: Points of discontinuity are x=0 ,x=-1, both are discontinuities of the second kind (essential discontinuities)

Jeffrey Jordon · Accepted Answer

Answer is given below (on video)

Identify the location of any discontinuities of f (x) attached For each di

Answered question

Answer & Explanation

New Questions in Calculus 1