Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
KVPY2015MathematicsLimits

Let a>0 be a real number. Then the limit _ x 2 a^ x +a^ 3-x - (a²+a ) a^ 3-x -a^ x / 2 is

Options

  1. A2 a
  2. B- 4 3 a
  3. Ca²+a 2
  4. D2 3 (1-a)

Correct answer

D. 2 3 (1-a)

Step-by-step solution

_ x 2 a^ x +a^ 3-x - (a²+a ) a^ 3-x -a^ x / 2 _ x 2 (a^ x -a ) (a^ x / 2 -a ) (a^ x / 2 +a ) (a-a^ x / 2 ) (a²+a^ x +a^ x / 2 a ) _ x 2 - (a^ x -a ) (a^ x / 2 +a ) a²+a^ x +a^ x / 2 a = 2 3 (1-a)

Practice Limits on Quantrex Academy →

More from Limits

If _ x 0 ( p 2x + 1 - 2x x + x ) = 1 then the value of ' p ' is 2026_ x 2 ( 1 - x x ) is equal to 2026The value of _ x 3 [ 1 x-3 + 9x 27-x^3 ] is: 2026_ x 0 (1 - 2x)(3 + x) x 4x is equal to: 2026If _ x 3 ( x^2 - ax - 3b x - 3 ) = 5 , then a + b = 2026If f(x) = cases x^2 - 1 & if x 2 x + 1 & if x < 2 cases , then _ x 1 f(x) + _ x 2 f(x) = 2026_ x 4 2 2 -( x+ x)^3 1- 2 x = 2025Let [x] denote the greatest integer less than or equal to x . Then _ x 2⁺ ( [x]^3 3 - [ x 3 ]^3 )= 2025 Full Limits list All KVPY PYQs