F(x)= 11 if x > 10
4 if x = 10
-x+11 if 0 < equal x < 10
11 if x <0
1. lim x-> 10 from the left
2. lim x-> 10 from the right
3.lim x-> 0 from the left
4. lim x-> 0 from the right
5. lim x-> 0
To find the limits as x approaches certain values, we need to evaluate the function at those values. Let's calculate each of the limits step by step:
1. lim x-> 10 from the left:
To find this limit, we need to approach the value of 10 from the left side of the number line. In this case, the function is defined as 4 when x equals 10. Therefore, the limit is equal to 4.
2. lim x-> 10 from the right:
To find this limit, we need to approach the value of 10 from the right side of the number line. In this case, the function is also defined as 4 when x equals 10. So, the limit is again equal to 4.
3. lim x-> 0 from the left:
To find this limit, we need to approach the value of 0 from the left side of the number line. In this case, the function is defined as -x+11 when 0 < x < 10. So, as x approaches 0 from the left, the function becomes -0 + 11 = 11. Thus, the limit is 11.
4. lim x-> 0 from the right:
To find this limit, we need to approach the value of 0 from the right side of the number line. In this case, the function is defined as -x+11 when 0 < x < 10. As x approaches 0 from the right, the function becomes -0 + 11 = 11. Consequently, the limit is 11.
5. lim x-> 0:
To find this limit, we need to consider the limit as x approaches 0 without specifying a direction (from the left or right). In this case, the limit cannot be determined since both the left-hand limit and the right-hand limit are different. From the left, the limit is 11, but from the right, the limit is also 11. Since these two values are not equal, the overall limit as x approaches 0 cannot be defined.
So, the answers are:
1. lim x-> 10 from the left = 4
2. lim x-> 10 from the right = 4
3. lim x-> 0 from the left = 11
4. lim x-> 0 from the right = 11
5. lim x-> 0 does not exist (undefined)