Question

Evaluate limit of x(sqrt(1+x^-2)) as x approaches 0+.

Answer 1

?

Answer 2

Take all the terms into the radical and simplify.

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Answer 3

even the x on the outside?

Answer 4

The answer I get is 1, but the answer is -1

Answer 5

x . sqrt(1+1/x^2) = sqrt( x^2 + 1)
lim_0 sqrt( x^2 + 1) = 1

It is 1.

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Answer 6

Maybe the answer key is wrong?

Answer 7

xsqrt(1/x^2 +1) = xsqrt(1/x^2(x^2 + 1)) (take out 1/x^-2 as a common factor
x*1/x*sqrt(x^2 +1)
sqrt(0+1)=1

Answer 8

Sorry, I meant 1/x^2 (aka x^-2)

Answer 9

yeah, I understand. Thank you