Monotonicity doubt using LVMT
So I shared the photo of question and the solution.
In the solution it directly says a functions is continuous or nor or whether a functionsi differentiable. Is there any quick method to find whethere a function is continuous or not ? Or it is just solution doesn't show the whole process of finding it ?
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@Apu
Note for OP
+solved @user1 @user2... to close the thread when your doubt is solved. Mention the users who helped you solve the doubt. This will be added to their stats.No there isnt any such quick method u need to find out it out through the the basic method only
Although the functions given here are quite simple thats why the the process isnt shown in the solution ig
my limits are a little weak
can you show the process of
finding the limit of g(x)
When x tends to 0+, the given function aqcuires value 0, when function tends to 0-, the function tends to infinity and when x=0, g(x)=1. So the function is not continous.
Assuming [x] is g.i.f.
for g(x). (reason being at 0+ [0+]=0 and 0/0+=0, similarly for 0-)
As for h(x), the result is known.
k(x) can be re-written as (x+3)^{log_2(5)} now, log_2(5) is slightly greater than 2. So the graph will be slightly sharper than a parabola for all x>=-3.
So, that is continous.
+solved @SirLancelotDuLac @Real potato
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