f(x)= array c x+a 2 x, 0 x< 4 2 x x+b, 4 x< 2 a 2 x-b x, 2 x array . is continuous in [0…
Mathematics · JEE Main · NTA Exams — Limit, Continuity and Differentiability
\[f(x)=\left\{\begin{array}{c} x+a \sqrt{2} \sin x, 0 \leq x<\frac{\pi}{4} \\ 2 x \cot x+b, \frac{\pi}{4} \leq x<\frac{\pi}{2} \\ a \cos 2 x-b \sin x, \frac{\pi}{2} \leq x \leq \pi \end{array}\right.\] is continuous in \([0, \pi]\), then
- \(a=-\frac{\pi}{6}, b=-\frac{\pi}{12}\)
- \(a=\frac{\pi}{6}, b=\frac{\pi}{12}\)
- \(a=\frac{\pi}{6}, b=-\frac{\pi}{12}\)
- \(a=-\frac{\pi}{6}, b=\frac{\pi}{12}\)
Answer
(A) a=- 6 , b=- 12
Sign up free on Edukali to view the step-by-step worked solution and practice thousands of similar questions.
Related practice questions
- Let [t] denote the greatest integer ≤ t and _ x 0 x [ 4 x ]=A . Then the function, f(x)= [x^ 2 ] ( x) is…
- If A > 0, B > 0 and A + B = 3 , then the maximum value of tan A tan B is
- Which of the following pair (s) of curves is/are orthogonal.
- The value of _ x 0 e^ x + (1+x)-(1-x)^ -2 x^ 2 is equal to
- Let p= _ x 1^ + (1+ ^ 2 x )^ 1 2 x then log p is equal to:
- The function f(x)= ^ -1 x+x increases in the interval
- If f_ n (x)=e^ f_ n-1 |x| for all n ∈ N and f_ n (x)=x , then d d x f_ n (x) is equal to:
- If f(x)= array c 1- 4 x x^ 2 , x 0 array . then at x = 0
More Limit, Continuity and Differentiability questions · Browse all practice questions