If x=t2 , y=t3 , then d2y / dx2 = _______ .
3/2
3/4t
3/2t
3t/2
it f(x) does not exist x→ 0+1
Lt f(x) doesnot exist x→0-
Lt x→0f(x) does not exist
Let f and g be differentiable functions satisfying g ' (a) =2 , g(a) =b and fog=I (identity function) .Then f ' (b) is equal to _______ .
1/2
2
2/3
None of these
2/1+x2
2x/1+x2
-2/1+x2
If f(x)=x+2 when x ≤ 1 and f(x)=4x-1 when x>1,then
f(x) is continuous at x=1
f(x) is discontinuous at x=0
If f(x) =[x]+[-x],x≠2 = λ ,x=2then f is continuous at x=2 , provided λ is equal to ______ .
1
0
-1
Let the function f be defined by f(x) =x sin 1/x , when x≠0
=0 , when x=0then at x=0,f is _____ .
continuous
not continuous
not defined
a+b/2
is continuous at x=a
is not continuous at x=a
has a limit when x→a and it is equal to lm
has a limit when x→a but it is not equal to lm
If x=at2 , y=2at ,then d2y / dx2 = ________ .
-1/t2
1/2at3
-1/t3
-1/2at3
Given f (x) = 4x8 , then
f(1/2)=f ' (-1/2)
f(-1/2) = f(1/2)
f ' (x) = f ' (-1/2)
f ' (1/2) = f ' (-1/2)