3sry abhi for talking hindi dat much badly.
1) Evaluate limx->infinity cosx/x or explain why it doesnt exist?
2) Evaluate lim t->4 (t-√3t+4)/t-4 or explain why it doesnt exist?
3) Evaluate lim x->13√ x-1/√x-1 or explain why it doesnt exist?
4) Let f(x)= sinx/x if x#0
f(x)= 1/2 if x=0
Discuss the continuity of f(x) and Sketch.........
Plz Give the Answers
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58 Answers
11SANKAR put 1/x =t now the ques becomes limx>infinity sint/t
so the answer is 0
33where its wrong...
definition of limit:
as x approaches a certain quantity... (always keeping itself in the domain of the function....) then if f(x) approaches a certain fixed quantity.. then that quantity approached by f(x) is called limit of function.
11REMEMBER THAT COS X LIES BETWEEN -1 TO 1
THERE SHOULD BE NO CONFUSION
33@shankara...
but cos(x)/x approaches a fixed quantity... zero...
33we should talk tommorow on this topic...
today i think my mind is sleeping for an hour...
Byee talk to u all tommorow... [1]
3yes philip u r rite can u pls explain.
in this qn also wont sin(∞)=undefined
11REMEMBER THAT COS X AS WELL AS SINX LIES BETWEEN -1 TO 1
THERE SHOULD BE NO CONFUSION
33sorry.. i had to go to sleep.. i forgot that... talk to u all, later
1no maybe i am wrong even now i think it should have been 0 idont know why i wrote inf there [7] sorry but i really think answer is 0
11priyam ur ques is diff as limx>0 sinx could be written as x
but not in ur case
3if u have some confusion may be the defn of limits can help u.
if it is not helping then draw a graph using a software
33@shankara...
Lim xsin(1/x) =0
x→0
Lim cos(x) =0
x→0 x
apply sandwitch theorem to both..
39hey guys use expansion of sinx and cosx and answer is at your feet.