Saved Bookmarks
| 1. |
Which of the following is True?A. if `f(x)` is continuous at `x=c` and `g(x)` is discontinuous at `x=c` then `(f.g)(x)` must be discontinuousB. If `f(x)` is continuous at `x=c` and `g(x)` is discontinuous at `x=c` then `(f.g)(x)` may be continuous.C. If `f(x)` and `g(x)` are discontinuous at `x=c`, then the product function must be discontinuous.D. If `f(x)` and `g(x)` are discontinuous at `x=c`, then the product function may be continuous. |
|
Answer» Correct Answer - B::D (A) & (B) Let `f(x)=x,xepsilonR` & `g(x)={("sin"(pi)/x,x!=0),(0,x=0):}` `f(x)` is continuous at `x=0` but `g(x)` is not. Now, `(f.g)(x)={(x"sin"(pi)/x,x!=0),(0, "at" x=0):}` is continuous at `x=0` (C) & (D) Let `f(x)={(0, xepsilonQ),(1,x!inQ):} , g(x) {(1,xepsilonQ),(0,x!inQ):}` `f(x)` & `g(x)` both are discontinuous everywhere. but `f(x).g(x)=0,xepsilonR` |
|