Find the indicated limits. If the limit does not exist, so state, or use the symbol + ∞ or - ∞. f(x) = { 5 if x ≤ 3 and 3 if x > 3
A.Lim f(x) x tends to 3+
B.Lim f(x) x tends to 3-
C.Lim f(x) x tends to 3
D.Lim f(x) x tends to ♾️
E.Lim f(x) x tends to - ♾️
If someone knows please help me
SKETCH IT !!!
step down from 5 to 3 at x = 3
To find the indicated limits of the function f(x) = { 5 if x ≤ 3 and 3 if x > 3, you can use the definitions of one-sided limits and the limit at infinity.
A. Lim f(x) as x approaches 3+ (from the right):
This means we need to find the limit as x approaches 3 from values greater than 3. In this case, for x > 3, f(x) is always equal to 3. Therefore, the limit of f(x) as x approaches 3 from the right is 3.
B. Lim f(x) as x approaches 3- (from the left):
This means we need to find the limit as x approaches 3 from values smaller than 3. In this case, for x ≤ 3, f(x) is always equal to 5. Therefore, the limit of f(x) as x approaches 3 from the left is 5.
C. Lim f(x) as x approaches 3 (two-sided limit):
Since the limit from both the left and right sides exist and are equal to 3 and 5 respectively, the limit of f(x) as x approaches 3 is undefined. We can say that the limit does not exist.
D. Lim f(x) as x approaches infinity:
This limit explores the behavior of the function as x goes towards positive infinity. In this case, as x goes towards positive infinity, f(x) is always equal to 3 (for x > 3). Therefore, the limit of f(x) as x approaches positive infinity is 3.
E. Lim f(x) as x approaches negative infinity:
This limit explores the behavior of the function as x goes towards negative infinity. In this case, since x < 3 for all values of x less than 3, f(x) is always equal to 5. Therefore, the limit of f(x) as x approaches negative infinity is 5.
To summarize:
A. Lim f(x) as x approaches 3+ = 3
B. Lim f(x) as x approaches 3- = 5
C. Lim f(x) as x approaches 3 does not exist
D. Lim f(x) as x approaches infinity = 3
E. Lim f(x) as x approaches negative infinity = 5