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.