Use app×
Join Bloom Tuition
One on One Online Tuition
JEE MAIN 2025 Foundation Course
NEET 2025 Foundation Course
CLASS 12 FOUNDATION COURSE
CLASS 10 FOUNDATION COURSE
CLASS 9 FOUNDATION COURSE
CLASS 8 FOUNDATION COURSE
0 votes
143 views
in Limits by (28.9k points)
closed by

Evaluate the following limit : \(\lim\limits_{\text x \to 1}\cfrac{\text x^3+1}{\text x+1} \)

lim(x→-1) (x3 + 1)/(x + 1)

1 Answer

+1 vote
by (29.8k points)
selected by
 
Best answer

We need to find the limit for : \(\lim\limits_{\text x \to 1}\cfrac{\text x^3+1}{\text x+1} \)

As limit can’t be find out simply by putting x = –1 because it is taking indeterminate form(0/0) form, so we need to have a different approach.

Let, Z = \(\lim\limits_{\text x \to 1}\cfrac{\text x^3+1}{\text x+1} \)

Note: To solve the problems of limit similar to one in our question we use the formula mentioned below which can be derived using binomial theorem.

Formula to be used: \(\lim\limits_{\text x \to a}\cfrac{(\text x)^n-(a)^n}{\text x-a} \) = nan -1

As Z does matches exactly with the form as described above so we don’t need to do any manipulations–

Use the formula: \(\lim\limits_{\text x \to a}\cfrac{(\text x)^n-(a)^n}{\text x-a} \) = nan -1

∴ Z = 3(–1)3–1 = 3

Hence, \(\lim\limits_{\text x \to 1}\cfrac{\text x^3+1}{\text x+1} \) = 3

Related questions

Welcome to Sarthaks eConnect: A unique platform where students can interact with teachers/experts/students to get solutions to their queries. Students (upto class 10+2) preparing for All Government Exams, CBSE Board Exam, ICSE Board Exam, State Board Exam, JEE (Mains+Advance) and NEET can ask questions from any subject and get quick answers by subject teachers/ experts/mentors/students.

Categories

...