lim (squar(14+y)-squar(14))/y

y->0

Find limit if there is one.

You mean????

[(14+y)^2 - 14^2 ] / y ????
if so
[ (14+y-14)(1+y+14)] / y

y (y+15)/ y

y+15

as y--->0
15

multipy the lim by sqrt(14+y)+sqrt14/same

lim (14+y - 14) /y(sqrt(14+y)+sqrt14))

y/y2sqrt14 =1/2sqrt14

To find the limit of the function:

lim (sqrt(14+y) - sqrt(14)) / y
y->0

First, let's try to simplify the expression. We can use the binomial theorem to do that. The binomial theorem states that for any real number a and b, and any positive integer n:

(a + b)^n = a^n + (nC1)a^(n-1)b + (nC2)a^(n-2)b^2 + ... + (nCn-1)ab^(n-1) + b^n

Using this theorem, we can rewrite sqrt(14+y) - sqrt(14) as:

sqrt(14+y) - sqrt(14) = [(14 + y) - 14] / [sqrt(14+y) + sqrt(14)]

Now, the expression can be simplified as:

[(14 + y) - 14] / [sqrt(14+y) + sqrt(14)] = y / [sqrt(14+y) + sqrt(14)]

Now, let's find the limit of this expression as y approaches 0:

lim (y / [sqrt(14+y) + sqrt(14)])
y->0

To evaluate this limit, we can substitute the value of y into the expression:

lim (0 / [sqrt(14+0) + sqrt(14)]) = 0 / [sqrt(14) + sqrt(14)] = 0 / [2sqrt(14)] = 0

Therefore, the limit of the given function is 0.