Determine if the following functions are continuous or discontinous at the given value of x.
1. f(x)= 3x+2x+1 at x= -2
2. f(x)= 9x2-1 at x=1
3. f(x)= 1/x-2 at x=2
4. f(x)= x-1/x^2 -1 at x=1
5. h(x)= x+1/x-1at x=1
6. f(x)= x^2 -2x+1 at x=3
7. f(x)= x/(x+2)(x-3) at x=2
8. f(x)= |x| at x=0
9. f(x) Cube root√x^2 -4 at x=5
10. f(x)= x+1/x-1 at x=0
1. Since "any polynomial function is continuous everywhere", is continuous everywhere and hence continuous at x = -2
2. Since is a polynomial, it is continuous at x = 1.
3. The function is discontinuous at x = 2 and it is an infinite discontinuity.
4. For the function , since both the numerator and the denominator are continuous, the discontinuities are the points obtained from , where is a removable discontinuity since, becomes continuous at .
5. The function is discontinuous at x = 1, since .
6. The function is continuous at x=3 as it is a polynomial function.
7. Since both numerator and denominator of the function are continuous, the points of discontinuity are, , i.e., . Therefore, is continuous at .
8. .
We know that f(x) is continuous at x = 0 if .
Now,
and . Hence f(x) is continuous at x = 0.
9. Since is a polynomial which is continuous everywhere, is continuous at x = 5.
10. For the function the point of discontinuity is x= 1, and hence f(x) is continuous at x = 0.
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