The value of _ x 2 [1^ 1 / ^ 2 x +2^ 1 / ^ 2 x + +n^ 1 / ^ 2 x ]^ ^ 2 x is
Mathematics · JEE Advanced · NTA Exams — Limit, Continuity and Differentiability
The value of
\[\lim _{x \rightarrow \frac{\pi}{2}}\left[1^{1 / \cos ^{2} x}+2^{1 / \cos ^{2} x}+\ldots+n^{1 / \cos ^{2} x}\right]^{\cos ^{2} x}\] is
\[\lim _{x \rightarrow \frac{\pi}{2}}\left[1^{1 / \cos ^{2} x}+2^{1 / \cos ^{2} x}+\ldots+n^{1 / \cos ^{2} x}\right]^{\cos ^{2} x}\] is
- 0
- n
- ∞
- \(\frac{\mathrm{n}(\mathrm{n}+1)}{2}\)
Answer
(B) n
Sign up free on Edukali to view the step-by-step worked solution and practice thousands of similar questions.
Related practice questions
- The function f(x)= ( +x) (e+x) is
- by appropriately matching the information given in the three columns of the following table. Let f ( x ) = x…
- If α, β are the roots of the quadratic equation ax 2 + bx + c = 0 then, Limit _ x 1- (a x^ 2 +b x+c ) (x- )^…
- Let f(x)= 1-x^ n+1 1-x and g (x) = 1 – 2 x + 3 x^ 2 - .........+ (–1) n n +1 x ^ n . Then the constant term…
- Suppose f(x) = e ax + e bx , where a ≠ b, and that f ”(x) – 2f ’ (x) –15f(x) = 0 for all x. Then the product…
- Let g(x)= (x-1)^ n ^ m (x-1) ; 0 x m and n are integers, m ≠ 0, n > 0, and let p be the left hand derivative…
- Let f : R → R be such that f (1) = 3 and f ′(1) = 6, then _ x 0 ( f(1+x) f(1) )^ 1 x equals
- Let f (x) be a polynomial function of second degree. If f (1) = f (–1) and a, b, c are in AP, then f ′ (a )…
More Limit, Continuity and Differentiability questions · Browse all practice questions