Determine whether the function is continuous at the given point. Show your solution. k(x)=x2x3+1 at x=-1

Question

Determine whether the function is continuous at the given point. Show your solution.  k(x)=x2x3+1 at x=-1

saiyansruleA · Accepted Answer

This question is taken from the continuity and discontinuity in which we have to check whether a given function is continuous at the given point or not continuous, so we can write the given function below k(x)=x2x3+1 check it at x=-1 is continuous or not First, we are written the given function and check whether it is continuous at a given point or not, so we have to check the left hand and right-hand limit (LHL and RHL)are equal or not, Given a function k(x)=x2x3+1 so formula we write it below at the given point LHL=limx→−1−k(x) RHL=limx→−1+k(x) and applicable only limits are exist otherwise discontinuous RHL=LHL=k(−1) if the above formula is satisfy then the given function is continuous now we calculate the L.H.L LHL=limx→−1−k(x) k(x)=x2x3+1 LHL=limx→−1−x2x3+1 now change the limit x=-1-h and h→0 LHL=limx→−1−x2x3+1 LHL=limh→0(−1−h)2(−1−h)3+1 LHL=limh→0(1+h2+2h)(−1−h3−3h2−3h+1) put the limits to check indetermine form LHL=1+02+2×0(−1−03−3×02−3×0+1)=1(−1+1)=10=underfine so the left hand limit does not exist similarly, we check for the RHL RHL=limx→1+k(x) k(x)=x2x3+1 RHL=limx→−1+x2x3+1 now change the limit x=−1+h and h→0 RHL=limx→−1+x2x3+1

Jeffrey Jordon · Accepted Answer

Answer is given below (on video)

Determine whether the function is continuous at the given point. Show your solut

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Answer & Explanation

New Questions in Calculus 1