find the value of k , function is continuous at x=2,

f(x)={ √5x+2 - √4x+4/ x-2.
x (not equal) 2
k. x =2 }

Dear Student,
Please find below the solution to the asked query:

We have:fx=5x+2-4x+4x-2x2kx=2If function is continuous at x=2, thenlimx2 fx=f2limx2 fx=klimx2 5x+2-4x+4x-2=klimx2 5x+2-4x+4x-25x+2+4x+45x+2+4x+4=klimx2 5x+2-4x+4x-215x+2+4x+4=k  a+ba-b=a2-b2limx2 5x+2-4x-4x-215x+2+4x+4=klimx2 x-2x-215x+2+4x+4=klimx2 15x+2+4x+4=kApplying limit we get: 110+2+8+4=k 112+12=kk=1212=143 As 12=23k=143

Hope this information will clear your doubts about this topic.

If you have any doubts just ask here on the ask and answer forum and our experts will try to help you out as soon as possible.
Regards

  • 6
it should be √5x + 2 and √4x + 4 in the first line
  • -1
What are you looking for?