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Lim (√(x-2)+√x-√2)/√(x^2-4) x--->2 Thank you for answering the last question. Please answer this too.

Lim  (√(x-2)+√x-√2)/√(x^2-4)
x--->2
Thank you for answering the last question. Please answer this too.

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2 Answers

Aditya Gupta
2081 Points
4 years ago
hello feba, this is an ez ques.
M= lim (√(x-2)+√x-√2)/√(x^2-4)= lim (√(x-2)+√x-√2)/√(x – 2)√(x+2)
= [1/√(2+2)]*lim (√(x-2)+√x-√2)/√(x – 2)
= ½ *lim (√(x-2)+√x-√2)/√(x – 2)
= ½ *(lim 1 + (√x-√2)/√(x – 2))
= ½ *[1+lim(√x-√2)/√(x – 2))]
now to find L= lim(√x-√2)/√(x – 2)), multiply and divide by √x + √2 we get
L= lim (x – 2)/[√(x – 2)(√x + √2)]= lim √(x – 2)/(√x + √2)= 0 at x tending to 2.
hence, M= ½ = 0.5
kindly approve :)
Saurabh Koranglekar
askIITians Faculty 10335 Points
4 years ago
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