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
To determine if a function is discontinuous, you need to check for any points where there may be a break or jump in the function's graph.
For the first function, f(x) = |x+2|, the absolute value function is continuous everywhere except at the point where the argument inside the absolute value becomes zero. So, in this case, we need to find the value of x that makes (x+2) equal to zero.
Solving (x+2) = 0, we get x = -2. Therefore, the function f(x) = |x+2| is discontinuous at x = -2 since it creates a jump or break in the function's graph.
For the second function, f(x) = e^xsinx, both the exponential function e^x and the sine function sinx are continuous everywhere. Since the product of two continuous functions is also continuous, the function f(x) = e^xsinx is continuous for all values of x. Hence, there are no points of discontinuity for this function.
In summary:
1. The function f(x) = |x+2| is discontinuous at x = -2.
2. The function f(x) = e^xsinx is continuous for all values of x.