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CBSE Questions for Class 11 Engineering Maths Limits And Derivatives Quiz 11 - MCQExams.com

The value of limx0(sin3xtanx)4 is
  • 0
  • 81
  • 4
  • 1
The value of limxsinπ4xcosπ4x is
  • π/4
  • π/2
  • 0

Given that f(x)
is a differentiable function of x and that f(x) . f(y) =  f(x)+ f(y) + f(xy)2 and that
f(2)=5.

Then f(3) is equal to?

  • 6
  • 24
  • 15
  • 19
lf f(x)=g(x) and g(x)=f(x) for all x and f(2)=4=g(2), then f2(24)+g2(24) is
  • 32
  • 24
  • 64
  • 48
Assertion(A): Let f(x) be twice differentiable function such that f(x)=f(x) and f(x)=g(x). lf h(x)=[f(x)]2+[g(x)]2 and h(1)=8, then h(2)=8

Reason (R): Derivative of a constant function is zero.
  • Both A and R are true R is correct reason of A
  • Both A and R are true R is not correct reason of A
  • A is true but R is false
  • A is false but R is true
Assertion (A): lf f(x)=cos2x+cos2(x+π3)cosxcos(x+π3) then f(x)=0

Reason(R): Derivative of constant function is zero
  • Both A & R are true, R is correct explanation for A
  • Both A & R are true,R is not correct explanation for A
  • A is true but R is false
  • A is false but R is true

 Let f(x)={xnsin1x,x00,x=0 , then f(x) is continuous but not differentiable at x=0 if
  • n(0,1]
  • n[1,)
  • n(,0)
  • n=0
The graph of the function y=f(x) has a unique tangent at the point (ea,0) through which the graph passes then limxealoge{1+7f(x)}sinf(x)3f(x) is
  • 1
  • 2
  • 0
  • 1
f(x)=|x1|+|x3| then f(2)=
  • 2
  • 2
  • 0
  • 1
lf f(x)=x.sin1x for x0, f(0)=0 then?
  • f is continuous at x=0
  • f is differentiable at x=0
  • f(0) exists but f(0+) does not exist
  • f is discontinuous at x=0
lf f(x) is a quadratic expression which is positive for all real vaues of x and g(x)=f(x)+f(x)+f(x) then for any real value of x
  • g(x)<0
  • g(x)>0
  • g(x)=0
  • g(x)>_0
Let f be a twice differentiable function such that f(x)=f(x) and f(x)=g(x)..
If h(x)=[f(x)]2+[g(x)]2,h(1)=6 and h(0)=4 then h(4) is equal to?
  • 16
  • 12
  • 13
  • None of these
If y=ex+ex, then dydx is equal to
  • exex2x
  • exex2x
  • 12xy24
  • 12xy2+4
If for all x,y the function f is defined by; f(x)+f(y)+f(x)f(y)=1 and f(x)>0.When f(x) is differentiable f(x)=,
  • 1
  • 1
  • 0
  • cannot be determined
The function f(x)=ex+x being differentiable and one to one, has a differentiable inverse f1(x), then find ddx(f1(x)) at the point f(loge2).
  • 13
  • 1
  • 3
  • 0
Given, f(x)=x33+x2sin1.5axsinasin2a5arcsin(a28a+17), then
  • f(x) is not defined at x=sin8
  • f(sin8)>0
  • f(x) is not defined at x=sin8
  • f(sin8)<0
If y+x+yx=c (where c0), then dydx has the value equal to
  • 2xc2
  • xy+y2x2
  • yy2x2x
  • c22y
Let f be a twice differentiable such that f(x)=f(x) and f(x)=g(x). If h(x)={f(x)}2+{g(x)}2, where h(5)=11. Find h(10)
  • 1
  • 10
  • 11
  • 100
 Let f(x)=x+tan1x,g(x)=x1+x2(x>0) Then
  • f(x)<g(x),x>0
  • f(x)>g(x),x>0
  • f(x)<g(x) in [1,)
  • None of these
Find the derivative of |x|+a0xn+a1xn1+a2xn2+....+an1x+an
  • x|x|+na0xn1+(n1)a1xn2+(n2)a2xn3+....+an1
  • 1+na0xn1+(n1)a1xn2+(n2)a2xn3+....+an1
  • x|x|+na0xn1+(n1)a1xn2+(n2)a2xn3+....+an
  • None of these
If f(x)=x+22x4+x22x4, then the value of 10f(102+) is
  • 1
  • 0
  • 1
  • Does not exist
Let f(x) be a polynomial function of second degree.If f(1)=f(1) and  a,b,c are in A.P f(a),f(b),f(c) are in 
  • G.P.
  • H.P.
  • A.G.P
  • A.P.
If ϕ(x)=limnx2nf(x)+g(x)1+x2n, then
  • ϕ(x)=g(x) for all x R
  • ϕ(x)=f(x) for all x R
  • {g(x)for1<x<1f(x)for|x|1
  • {g(x)for|x|<1f(x)for|x|>1f(x)+g(x)2for|x|=1
Let f(x)=x1+x+2410x1,1x26 be a real valued function, then f(x) for 1<x<26 is
  • 0
  • 1x1
  • 2x1
  • 1
If cos4θx+sin4θy=1x+y then dydx=
  • xy
  • tan2θ
  • 0
  • (x2+y2)sec2θ
Let f be a differentiable function satisfying f(x)+f(y)+f(z)+f(x)f(y)f(z)=14 for all x, y, zR
Then,
  • f(x)<0 for all xR
  • f(x)=0 for all xR
  • f(x)>0 for all xR
  • none of these
Given  f(x)=x33+x2sin1.5axsina.sin2a5arcsin(a28a+17) then :
  • f(x) is not defined at x=sin8
  • f(sin8)>0
  • f(x) is not defined at x=sin8
  • f(sin8)<0
Suppose, A=dydx of x2+y2=4 at (2,2),B=dydx of siny+sinx=sinxsiny at (π,π) and C=dydx of 2exy+exeyex=exy+1 at (1,1), then (ABC) has the value equal to .....
  • 12
  • 13
  • 1
  • 2
Suppose A=dydx when x2+y2=4 at (2,2),B=dydx when siny+sinx=sinxsiny at (π,π) and C=dydx when 2exy+exeyexey=exy+1 at (1,1), then (A+B+C) has the value equal to 
  • 1
  • e
  • 3
  • 0
If limxa(f(x)+g(x))=2 and limxa(f(x)g(x))=1
then the value of limxaf(x)g(x) is?
  • Does not exist
  • Exists and is 34
  • Exists and is 34
  • Exists and is 43
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