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CBSE Questions for Class 12 Commerce Maths Continuity And Differentiability Quiz 15 - MCQExams.com

if the function f(x)={a+sin1(x+b),x1x,x<1 is differentiable at x=1, then ab is equal to 
  • 1
  • 0
  • 1
  • 2
The function f(x)=x1+|x| is differentiable at which of the following?
  • Every where
  • Everywhere except at x=1
  • Everywhere except at x=0
  • Everywhere except at x=0 or 1
If y=esin1(t21) & x=esec1(1t21), then dydx is equal to
  • xy
  • yx
  • yx
  • xy
If f(x)=sin1[2x1+x2],then f(x) is differentiable on 
  • [-1,1]
  • R-{-1,1}
  • R-(-1,1)
  • None of these
f(X)=|x|+|x-1| is continuous at 
  • '0' only
  • 0,1 only
  • Every where
  • No where
If fn(x)=efn1(x) for all nϵN and f0(x)=x then ddx{fn(x)} is equal to 
  • fn(x).ddx{fn1(x)}
  • fn(x).fn1(x)
  • fn(x).fn1(x).....f2(x).f1(x)
  • ni=1fi(x)
The order of the differential equation of all circles whose radius is 4, is?
  • 1
  • 2
  • 3
  • 4
If f(x)=|x||sinx|, then f(π4) is equals
  • (π4)1/2(22ln4π22π)
  • (π4)1/2(22ln4π+22π)
  • (π4)1/2(22lnπ4+22π)
  • None of these.
Let f:(1,1)R be a differentiable function satisfying 
             (f(x))4=16(f(x))2 for all x(1,1)
   f(0)=0
The number of such functions is 
  • 2
  • 3
  • 4
  • more than 4
If y=(1+t2)(1t2)(1+t2)+(1t2) and x=(1t4) , then dydx
  • 1t2{1+1t4}
  • {(1t4)1}t6
  • 1t2{1+(1t4)}
  • 1(1t4)t6
f(x) is diffrentiable function and (f(x). g(x)) is differentiable a x=a , then 
  • g(x) must be differentiable at x=a
  • if g(x) is discontinuous , then f(a) =0
  • f(a) 0 then g(x) must be differentiable
  • nothing can be said
Give that f(x) =xg(x) /|x| , g(0) = 0 and f(x) is continous at x=Then the value of f' (0)
  • Does not exist
  • is -1
  • is 1
  • is 0
Let f(x)=
1752636_53b9ea09cceb44beb34375cef34837d0.PNG
  • f' is differentiable
  • f is differentiable
  • f' is continuous
  • f is continuous
If f(x)={xlogcosxlog(1+x2),x00,x=0 then
  • f(x) is not continuous at x=0.
  • f(x) is continuous at x=0.
  • f(x) is continuous at x=0 but not differentiable at x=0.
  • f(x) is differentiable at x=0.
Let f: RR be a function such that f(x+y)= f(x)+f(y), x,yϵR. If f(x) is differentiable at x=0, then
  • f(x) is differentiable only in a finite interval containing zero
  • f(x) is continuous xϵR
  • f(x) is constant xϵR
  • f(x) is differentiable except at finitely many points
Let f(x) be a function satisfying f(x+y)=f(x)+f(y) and f(x)=xg(x) x, y R, where g(x) is a continuous function then, which of the following is true?
  • f(x)=g(0)
  • f(x)=g(0)
  • f(x)=g(0)
  • f(x)=g(0)
Which of the following is differentiable at x= 0
  • cos (|x|)+|x|
  • cos (|x|)|x|
  • sin(|x|)+|x|
  • sin(|x|)|x|
cos|x| is differentiable everywhere.
  • True
  • False
If the function f:[0,8]R is differentiable, then for0<a,b<2,80f(t)dt is equal to
  • 3[α3f(α2)+β2f(β2)]
  • 3[α3f(α)+β3f(β)]
  • 3[α2f(α3)+β2f(β3)]
  • 3[α2f(α2)+β2f(β2)]
Let f(x) and g(x) be differentiable for 0x1, such that f(0) such that f'(c)=2g'(c), then the value of g(1) must be 
  • 1
  • 3
  • -2
  • -1
f(x)=x2+xg(1)+g(2) and g(x)=f(1)x2+xf(x)+f(x)

The value of g(0) is
  • 0
  • -3
  • 2
  • None of these
f(x) is not invertible for
  • x[π2tan12,π2tan12]
  • x[tan112,π+tan112]
  • x[π+cot12,2π+cot12]
  • None of these
Let f(0,)R be a differentiable function such that f(x)=2f(x)x for all xϵ(0,) and f(1)1 Then
  • limx0+f(1x)=1
  • limx0+xf(1x)=2
  • limx0+x2f(1x)=0
  • |f(x)|2 for all xϵ(0,2)
0:0:1


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