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

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  • 6
it should be √5x + 2 and √4x + 4 in the first line
  • -1
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