Question

Given f(x)={0.122+206+15,0.25(13+k),​1x​, if the left-hand limit of f(x) is equal to the right-hand limit of f(x) as x approaches 10, the limit of f(x) as x approaches 10 is ________, and the value of k is ________.

Answer 1

The limit of f(x) as x approaches 10 is 221.122, and the value of k is 871.488.

Step-by-step explanation:

The left-hand limit of a function represents the value of the function as x approaches a specific value from the left side. The right-hand limit represents the value of the function as x approaches the same value from the right side. In this case, the left-hand limit and the right-hand limit of f(x) as x approaches 10 are equal. This means that the function approaches the same value from both sides of 10. The limit of f(x) as x approaches 10 is the value that the function approaches as x gets arbitrarily close to 10. To find the limit, we can substitute 10 into the function and simplify:

f(10) = 0.122 + 206 + 15 = 221.122.

So, the limit of f(x) as x approaches 10 is 221.122.

To find the value of k, we can substitute 10 into the function and solve for k:

0.25(13+k) = 221.122

Divide both sides by 0.25:

13 + k = 884.488

Subtract 13 from both sides:

k = 871.488.