If f(x)=x−4|x−4|+a,x<4a+b, x=4x−4|x−4|+b,x>4 Then, f(x) is continuous at x=4 when a2+b2=

If f(x)=x4|x4|+a,x<4a+b, x=4x4|x4|+b,x>4 Then, f(x) is continuous at x=4 when a2+b2=

    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:

    We have,

    limx4f(x)=limx4x4|x4|+a=limx4x4(x4)+a=a1limx4+f(x)=limx4+x4|x4|+b=limx4+x4x4+b=b+1

    and,f(4)=a+b

    If f(x) is continuous at x = 4, then

    limx4f(x)=f(4)=limx4+f(x)a1=a+b=b+1b=1 and a=1a2+b2=2

     f(|x|)=2x+1,x<02x+1,x0

    We find that f(x) is neither continuous nor differentiable at x = 0.. At all other points f(x) is continuous and differentiable. f(|x|)is every where continuous but not differentiable at x = 0.

    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.