Final answer:
To solve the limit &lim; ₓ→0 (√((x+3) - √3 ) / x), we can simplify the expression by multiplying the numerator and denominator by the conjugate of the numerator and we get √((3) + √3 ).
Step-by-step explanation:
To solve the limit &lim; ₓ→0 (√((x+3) - √3 ) / x), we can simplify the expression by multiplying the numerator and denominator by the conjugate of the numerator, which is √((x+3) + √3 ).
After simplifying and canceling out the x in the denominator, we are left with √((x+3) + √3 ).
Substituting x=0 into the expression gives us √(3+√3 ). Therefore, the limit is equal to √(3+√3 ).