SOLUTION: Evaluate the limit of each indeterminate quotient: {{{matrix(3,2, "", "", lim, (sqrt(5-x)-sqrt(3+x))/(x-1), "x->1", "" )}}}

Question 178429: Evaluate the limit of each indeterminate quotient:

Answer by Edwin McCravy(20055) (Show Source): You can put this solution on YOUR website!
Evaluate the limit of each indeterminate quotient:




The numerator has the square roots, so we 
multiply top and bottom by the conjugate of the
numerator, which is 



If you "FOIL" out the top the middle two terms
cancel and we get:







Factor  out of the numerator:




Write the expression in the parentheses on top in 
descending order:



Cancel the 's:






------------------------------------------------



Both the numerator and the denominator have 
square roots, so we multiply top and bottom by 
the conjugates of both numerator and denominator,
which is .

We'll reverse the order of those factors when we
multiply the bottom by it so the conjugates will 
be next to what they're the conjugates of:



"FOIL" out the first two terms in the top, and the 
two middle terms will cancel.  Do the same in the
bottom:













----------------------------------------





Factor  out of the top:







Edwin

RELATED QUESTIONS
Approximate the limit from a graph of the function, and then find the limit... (answered by Edwin McCravy)
Evaluate the limit if each indeterminate quotient: Hi! I just started calculus and these... (answered by stanbon)
find the limit: lim x approaches 3, 3 sqrt 2x^2 -10 Thank you (: (answered by ikleyn)
lim sqrt(x+3) - sqrt(3) /x x approches... (answered by Fombitz)
lim x -> 0 (sqrt x + 1)^2 - 1 /... (answered by solver91311)
evaluate: lim(x->4, sqrt... (answered by jsmallt9)
Evaluate the limit, if it exisit lim goes to -1 of 2x^2... (answered by solver91311)
Use the definition of limit to verify that: (1). lim x->3 (5-2x) = - 1 2). lim... (answered by solver91311)
{{{ sqrt x+2 - sqrt x-3 = 1... (answered by robertb)