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If lim(xto2) (tan(x-2).(x^(2)+(k-2)x-2k)...

If `lim_(xto2) (tan(x-2).(x^(2)+(k-2)x-2k))/((x^(2)-4x+4))=5`, then find the value of k.

Text Solution

Verified by Experts

The correct Answer is:
3
We have `underset(xto2)lim(tan(x-2).(x^(2)+(k-2)x-2k))/((x-2)^(2))=5`
`impliesunderset(xto2)lim(tan(x-2))/(x-2).((x^(2)+(k-2)x-2k))/(x-2)=5`
`impliesunderset(xto2)lim(x ^(2)+(k-2)x-2k)/(x-2)=5`
`impliesx^(2)+(k-2)x-2k=(x-2)(x+k)`
For the value of limit to be 5, k=3
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