SOLUTION: Suppose f(x) is defined as shown below f(x) ={e^x if x ≥ 0 {x + 1 if x < 0 Determine whether or not that f is continuous at 0.

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Question 1158629: Suppose f(x) is defined as shown below
f(x) ={e^x if x ≥ 0
{x + 1 if x < 0
Determine whether or not that f is continuous at 0.
Found 2 solutions by Shin123, MathLover1:
Answer by Shin123(626) About Me  (Show Source):
You can put this solution on YOUR website!
When x is 0, f(x) is 1. If x is very slightly below 0, f(x) is very close to 1. As x gets closer and closer to 0, but never reaches 0, f(x) gets closer and closer to 1, but never reaches 1. f(x) is continuous at 0. Here is a graph,

Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
Suppose f%28x%29 is defined as shown below
f%28x%29+=e%5Ex if x+%3E=0
........x+%2B+1 if x+%3C+0

Determine whether or not that f is continuous at 0.

for the values of x+%3E=0, we have to select the function f%28x%29++=+e%5Ex

right-hand limit: (x comes from the right, x+%3E+a)
lim%28x-%3E0%2C+f%28x%29+%29=+lim+%28x-%3E0%2Ce%5Ex+%29=1.......a)

for the values of+x%3C+0, we have to select the function+f%28x%29++=x+%2B+1
left-hand limit: (x comes from the left, x+%3C+a)

lim+%28x-%3E0%2Cx%2B1%29=1..........b)

lim+%28x-%3E0%2Ce%5Ex+%29=+lim+%28x-%3E0%2Cx%2B1%29

Hence the function is continuous at x+=+0.