It says find the numbers, if any, at which the given function is discontinuous.
f(x)=abs(x+2)
*abs - absolute value
f(x)=e^xsinx
for both of these problems i saw that it was continuous but i don't really know
Both are continous.
Thank you so much bobpursley!!!
To determine if a function is discontinuous, you need to look for any points where there might be a break or jump in the graph. In the case of the given functions, we'll analyze them one by one:
1. Function: f(x) = |x + 2| (absolute value)
To check for any discontinuities in this function, we need to consider the behavior around the values of x where there may be potential breaks.
- At x = -2, the function involves the absolute value of (-2 + 2), which is zero. Absolute value functions are continuous everywhere except at zero. So, f(-2) = |0| = 0.
In this case, the function is continuous at x = -2 since f(-2) = 0, which means there are no jumps or breaks in the graph.
2. Function: f(x) = e^x * sinx
To check for any discontinuities in this function, we need to consider the behavior around the values of x where there may be potential breaks.
- We know that both the exponential function, e^x, and the trigonometric function, sinx, are continuous everywhere. So, their product, f(x) = e^x * sinx, is also continuous everywhere.
In this case, the function is continuous for all values of x, which means there are no jumps or breaks in the graph.
Therefore, for both functions f(x) = |x + 2| and f(x) = e^x * sinx, they are continuous on their entire domain. There are no numbers at which these functions are discontinuous.