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Question

Let f:RR be defined as
f(x)=⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪λ|x25x+6|μ(5xx26),x<2e tan(x2)x[x],x>2 μ ,x=2
where [x] is the greatest integer less than or equal to x. If f is continuous at x=2, then λ+μ is equal to

A
1
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B
e(e2)
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C
e(e+1)
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D
2e1
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