Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
NDA2023MathematicsLimitsActual

What is _ x 1 x^9-1 x^3-1 equal to?

Options

  1. A-1
  2. B-3
  3. C3
  4. DLimit does not exist

Correct answer

C. 3

Step-by-step solution

_ x 1 x^9-1 x^3-1 _ x 1 (x^3 )^3-1 x^3-1 = _ x 1 (x^3-1 ) (x^6+x^3+1 ) x^3-1 = _ x 1 x^6+x^3+1=3

Practice Limits on Quantrex Academy →

More from Limits

What is _ x 1 x^ (n^2-1) -1 x^ (n+1) -1 equal to, where n>1 is a natural number ? 2026What is _ x 0 10^ x -1 x equal to ? 2026Consider the following for the two (02) items that follow: Let the function f(x) = x^2 + 9 . What is _ x 0 f(x) - 3 f(x)+7 - 4 equal to? 2025For the following three (03) items: Consider the function f(x) = x|x| . What is _ x -1 f(x) equal to? 2025For the following two (02) items: Let f(x) = cases 1 - 2x x^2 , & x 0 cases What is _ x 0^- f(x) equal to? 2025For the following two (02) items: Let f(x) = cases 1 - 2x x^2 , & x 0 cases What is _ x 0^+ f(x) equal to? 2025Consider the following for the two (02) items that follow: Let the function f(x) = [x] , where [ ] is the greatest integer function and g(x) = |x| . What is _ x 0 f(x) g(x) equal t 2025Consider the following for the two (02) items that follow: Let the function f(x) = [x] , where [ ] is the greatest integer function and g(x) = |x| . What is _ x 0 f(x) g(x) equal t 2025 Full Limits list All NDA PYQs