Theorems for Continuity
Trending Questions
True
False
If the function 'f' and 'g' are continuous at c then. Choose the incorrect alternative.
f + g is continuous at c
f - g is continuous at c
is continuous at c
f.g is continuous at c
Given f(x)=g(x).h(x). If g(x) and h(x) are continuous in a given interval then f(x) would also be continuous in the same interval.
True
False
f(x) and g(x) are continuous functions such that limx→a[3f(x)+g(x)]=6 and limx→a[2f(x)−g(x)]=4. Given that the function h(x).g(x) is continuous at x = a and h(a)=4, which of the following must be true?
limx→a−h(x) ϵ R and limx→a+h(x) ϵ R
limx→ah(x)=0
limx→ah(x)=4
limx→ah(x)=∞
f(x) and g(x) are continuous functions such that limx→a[3f(x)+g(x)]=6 and limx→a[2f(x)−g(x)]=4. Given that the function h(x).g(x) is continuous at x = a and h(a)=4, which of the following must be true?
limx→ah(x)=∞
limx→a−h(x) ϵ R and limx→a+h(x) ϵ R
limx→ah(x)=4
limx→ah(x)=0
- 0
- −12
- −124
- −148
then f(x) is continuous at x=π2, if
The function f(x)=cosx−sinxcos2x is not defined at x=π4 The value of f(π4) so that f(x) is continuous at x=π4 is
- 1√2
- √2
- −√2
- 1
- Is continuous but not differentiable
- Is having continuous derivative
- Is continuous
- Is continuous and differentiable