find the linear approximation to f(x)=sqrt 25-x^2 near 3

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I assume you are talking about the limit or the tan line?For the limit since F(x) is continuous there is a right and left limit so the limit exits and as x approaches 3 the limit is 4.For the tan line's slope you find the derivative (dx/dy) 1st :put 1/2 in front and then subtract 1 = 1/(2 sqrt 25- x^2)2nd : find the derivative of the stuff inside the () which gives you -x/sprt 25-x^2 ( the twos canceled out)Next plug in 3 which gives you 3/4 which is dx/dy at 3Hope this is what you need and good luck