1) lim x→0 j(x) = ? when j(x) = 3; x<0 and 9; x=0 and 3; x>0
2) lim x→1 h(x) = ? when h(x) = x^2 + 1; x<1 and 2√x; x>1
To find the limits in the given functions, we evaluate the function values as x approaches the given values.
1) For j(x) = 3; x < 0:
As x approaches 0 from the left side (x < 0), the function j(x) remains constant at 3. Therefore, the limit as x approaches 0 from the left is equal to 3.
For j(x) = 9; x = 0:
When x is exactly equal to 0, the function j(x) is equal to 9. Therefore, the limit as x approaches 0 is equal to 9.
For j(x) = 3; x > 0:
As x approaches 0 from the right side (x > 0), the function j(x) remains constant at 3. Therefore, the limit as x approaches 0 from the right is equal to 3.
2) For h(x) = x^2 + 1; x < 1:
As x approaches 1 from the left side (x < 1), the function h(x) can be evaluated by substituting x = 1 into the function: h(1) = 1^2 + 1 = 2. Therefore, the limit as x approaches 1 from the left is equal to 2.
For h(x) = 2√x; x > 1:
As x approaches 1 from the right side (x > 1), the function h(x) can be evaluated by substituting x = 1 into the function: h(1) = 2√1 = 2(1) = 2. Therefore, the limit as x approaches 1 from the right is equal to 2.
Note: It's important to consider both the left and right-hand limits separately because the function may have different behaviors on either side of the given value of x.