The value of c in Lagrange’s theorem for the function f(x)=logc⁡sin⁡x in the interval [π/6,5π/6], is

The value of c in Lagrange's theorem for the function f(x)=logcsinx in the interval [π/6,5π/6], is

  1. A

    π4

  2. B

    π2

  3. C

    2π3

  4. D

    none of these

    Register to Get Free Mock Test and Study Material

    +91

    Verify OTP Code (required)

    I agree to the terms and conditions and privacy policy.

    Solution:

    Clearly, f(x)=logsinx is continuous on [π/6,5π/6] and differentiable on (π/6,5π/6)Therefore, there exists c(π/6,5π/6) such that

    f(c)=f5π6fπ65π6π6 cotc=loge2+logc22π3 cotc=0c=π2(π/6,5π/6)

    Chat on WhatsApp Call Infinity Learn

      Register to Get Free Mock Test and Study Material

      +91

      Verify OTP Code (required)

      I agree to the terms and conditions and privacy policy.