Saved Bookmarks
| 1. |
f is a continous function in `[a, b]`; g is a continuous function in [b,c]. A function h(x) is defined as `h(x)=f(x) for x in [a,b) , g(x) for x in (b,c]` if f(b) =g(b) thenA. `h(b^(+))=g(b^(-))` and `h(b^(-))=f(b^(+))`B. `h^(b^(-))=g(b^(+))` and `h(b^(+))=f(b^(-))`C. `h(x)` can be made continuous at `x=b` by by defining it at the point `x=b`D. `f(a)=g(c)` |
|
Answer» Correct Answer - B::C `h(x)` is continous in `[a,b)cup(b,c]` `becauseh(b^(-))=f(b^(+))` are undefined `h(b^(-))=f(b^(-))=f(b)=g(b)=g(b^(+))` and `h(b^(+))=g(b^(+))=g(b)=f(b)=f(b^(-))` Hence `h(b^(-))=h(b^(+))=f(b)=g(b)` Thus, `h(x)` has removable discontinuity at `x=b` |
|