lim

x!0
k + cosmx
x2 = −4 .

FIND M AND X?

To find the values of m and x in the given expression:

1. Start by solving the equation x^2 = -4 for x. Since the equation has no real solutions (since the square of any real number cannot be negative), we can conclude that there are no real values of x that satisfy this equation.

2. Next, we have the limit expression lim (x approaches 0) of k + cos(mx). To find the value of m, we need to investigate the behavior of the expression as x approaches 0.

3. The value of cos(mx) oscillates between -1 and 1 as x approaches 0. So, the limit of cos(mx) as x approaches 0 depends on the value of m.

- If m = 0, cos(mx) will be equal to cos(0) = 1 for all x, and the limit expression simplifies to k + 1.
- If m ≠ 0, then cos(mx) cannot approach a single value as x approaches 0. Thus, the limit expression does not exist for any value of k.

Therefore, the value of x cannot be found, and the value of m can be either 0 or any non-zero real number.