Find k if the function f(x) is continuous at x=4.f(x)=cos pi/x, x>=4 f(x)=2square root x, x

Since you've not specified where is placed k, we'll assume
that f(x) = k`sqrt(x)`

For a function to be continuous at a
point x=a, it must obey the following rules:

1) f(a) must
exist

2) lim f(x) is
finite

x-> a

3) lim
f(x) = f(a)

x-> a

Now,
we'll determine the value of k, knowing that the function is
continuous.

lim cos `pi` /x = lim k`sqrt(x)` =
f(4)

x->4             
x->4

lim cos `pi` /x = cos `pi` /4 =
sqrt2/2

x->4

lim
k`sqrt(x)` = ksqrt4 =
2k

x->4

f(4) = cos ` `
/4 = sqrt2/2

We'll re-write the 3rd condition of
continuity:

sqrt2/2 = 2k => k =
sqrt2/4

The value of k for the given function
to be continuous is k = sqrt2/4.