JEE Questions for Maths Limits Continuity And Differentiability Quiz 3 - MCQExams.com


Maths-Limits Continuity and Differentiability-34880.png
  • 0
  • 3/5
  • 2
  • 5/3

Maths-Limits Continuity and Differentiability-34882.png
  • π/10
  • 3π/10
  • 3π/2
  • 3π/5
Discuss the continuity of the function f(x) = sin 2x - 1 at the point x = 0 and x = π
  • Continuous x = 0 and x = π
  • Discontinuous at x= 0 but continuous at x= π
  • continuous at x = 0 but discontinuous at x = π
  • Discontinuous at x = 0, π
The value of f at x = 0 , so that function
Maths-Limits Continuity and Differentiability-34885.png
  • 0
  • log 4 4
  • 4
  • e4

Maths-Limits Continuity and Differentiability-34887.png
  • a + b
  • a - b
  • a
  • b

Maths-Limits Continuity and Differentiability-34889.png
  • -6
  • 0
  • 1
  • -1
If f(x) = x(√x - √(x + 1)) , then f(x) is continuous in
  • [0, ∞)
  • (0, ∞)
  • (-∞, ∞)
  • (3,∞)

Maths-Limits Continuity and Differentiability-34892.png
  • -1
  • 1
  • 0
  • 2

Maths-Limits Continuity and Differentiability-34894.png
  • 1/3
  • 2/3
  • 3/2
  • 3

Maths-Limits Continuity and Differentiability-34896.png
  • 1
  • -1
  • 2
  • -2
  • 3
If a function f : R → R, where R is the set of real numbers satisfying the equation f(x + y) = f(x) + f(y), ∀< i>x, y. If f(x) is continuous at x = 0, then
  • f(x) is discontinuous, for all x ϵ R
  • f(x) is continuous, for all x ϵ R
  • f(x) is continuous for x ϵ {1,2,3,4}
  • None of the above
The function f(x) is defined by
Maths-Limits Continuity and Differentiability-34899.png
  • 0
  • 1/4
  • - (1/2)
  • None of these
Let [] denotes the greatest integer function and f(x) = [tan2 x]. Then,

  • Maths-Limits Continuity and Differentiability-34901.png
  • f(x) is continuous at x = 0
  • f(x) is not differentiable at x = 0
  • f(x) = 1
The points of discontinuity of tan x are
  • nπ, n ϵ I
  • 2nπ, n ϵ I
  • (2n+1)π/2, n ϵ I
  • None of these

Maths-Limits Continuity and Differentiability-34904.png
  • 1
  • -1
  • 0
  • 2

Maths-Limits Continuity and Differentiability-34906.png
  • a2
  • 2a2
  • 3a2
  • 4a2

Maths-Limits Continuity and Differentiability-34908.png
  • 0
  • 1/2
  • 1/4
  • - (1/2)
  • None of these
The function f(x) = x - |x - x2| is
  • continuous at x = 1
  • discontinuous at x = 1
  • not defined at x = 1
  • None of these

Maths-Limits Continuity and Differentiability-34911.png
  • f(x) is continuous at x = 0
  • f(|x|) is continuous at x = 0
  • f(x) is discontinuous at x = 0
  • None of these

Maths-Limits Continuity and Differentiability-34913.png
  • 1
  • 0
  • 1/2
  • -1
If the function f : R → R given by
Maths-Limits Continuity and Differentiability-34915.png
  • 4
  • 3
  • 2
  • 1

Maths-Limits Continuity and Differentiability-34917.png
  • 1
  • 0
  • 1/2
  • -1

Maths-Limits Continuity and Differentiability-34919.png
  • m = 1, n = 0
  • m = nπ/2 + 1
  • n = m π/2
  • m = n = π/2

Maths-Limits Continuity and Differentiability-34921.png
  • a = 0, b = 0
  • a = 1, b = 1
  • a = -1, b = 1
  • a = 1, b = -1

Maths-Limits Continuity and Differentiability-34923.png
  • continuous
  • discontinuous
  • differentiable
  • non - Zero

Maths-Limits Continuity and Differentiability-34925.png
  • 1
  • 1/2
  • -1/2
  • -1

Maths-Limits Continuity and Differentiability-34927.png
  • 1
  • -2
  • 2
  • 1/2

Maths-Limits Continuity and Differentiability-34929.png

  • Maths-Limits Continuity and Differentiability-34930.png
  • 2)
    Maths-Limits Continuity and Differentiability-34931.png

  • Maths-Limits Continuity and Differentiability-34932.png
  • f(x) continuous at x = 0
If f : R → R is defined by
Maths-Limits Continuity and Differentiability-34934.png
  • (1/2, 1/2)
  • (0, -1)
  • (0, 2)
  • (1, 0)

Maths-Limits Continuity and Differentiability-34936.png
  • 3
  • -3
  • e3
  • e-3

Maths-Limits Continuity and Differentiability-34938.png
  • 1/2 loge 2
  • loge 4
  • loge 8
  • loge 2
If f : R → R is defined by
Maths-Limits Continuity and Differentiability-34940.png
  • R
  • R - {-2}
  • R - {-1}
  • R - {-1, -2}

Maths-Limits Continuity and Differentiability-34942.png
  • x = 1 only
  • x = 1 and x = -1
  • x= 1 and x = -1 and x = -3
  • x = , x = - 1, x = -3 and other values of x

Maths-Limits Continuity and Differentiability-34944.png
  • discontinuous at origin because |x| is discontinuous
  • continous at origin
  • discontinuous at origin because both |x|and |x|/ x are discontinuous there
  • discontinuous at the origin because |x|/x is discontinuous there
The function represented by the following graph is
  • continuous but not differentiable at x = 1
  • differentiable but not continuous at x = 1
  • continuous and differentiable at x = 1
  • neither continuous nor differentiable at x = 1

Maths-Limits Continuity and Differentiability-34947.png
  • continuous for all values of x
  • discontinuous at x = π/2
  • not differentiate for some values of x
  • discontinuous at x = - 2
If f(x + y) = f(x) f(y) and f(x) = 1 + sin (3x) g(x), where g(x) is continuous , then f'(x) is equal to
  • f(x) g(0)
  • 3g(0)
  • f(x) cos 3x
  • 3f(x) g(0)
  • None of these
If f(x) is a differentiable function and f'(4) = 5. Then,
Maths-Limits Continuity and Differentiability-34950.png
  • 0
  • 5
  • 20
  • -20

Maths-Limits Continuity and Differentiability-34952.png
  • f(x) is continuous at x= 1
  • f(x) is not continuous at x = 1
  • f(x) is differentiable at x = 1
  • f(x) is not differentiable at x = 1
The function f(x) = |x - 1| is
  • continuous everywhere
  • continuous everywhere, except at x = 1
  • differentiable everywhere
  • differentiable nowhere
f(x) = x sin (1/x)
  • is continuous but not differentiable at x = 0
  • is discontinuous but differentiable at x = 0
  • is differentiable at x = 0
  • cannot be determined
f(x) = |x - 3|is...at x = 3
  • continuous and not differentiable
  • continuous and not differentiable
  • discontinuous and not differentiable
  • continuous and differentiable
Function f(x) = |x - 1|+ |x - 2|, x ϵ R is
  • differentiable everywhere in R
  • except x = 1 and x = 2 differentiable everywhere in R
  • not continuous at x = 1 and x = 2
  • increasing in R

Maths-Limits Continuity and Differentiability-34958.png
  • continuous and differentiable at x = 3
  • continuous at x = 3 but not differentiable at x = 3
  • continuous and differentiable everywhere
  • continuous at x = 1 but not differentiable at x = 1
If f(x) = |loge|, then f'(x) equals
  • 1/|x|, x ≠ 0
  • 1/x for |x| > 1 and -1/x for |x| < 1
  • -1/x for |x|> 1 and 1/x for |x| < 1
  • 1/x for x > 0 and - (1/x) for x = 0

Maths-Limits Continuity and Differentiability-34961.png
  • c = 0 and a = 2b
  • a = b and c ϵ R
  • a = b and c = 0
  • a = b and c ≠ 0

Maths-Limits Continuity and Differentiability-34963.png
  • -1/9
  • -2/9
  • -13
  • 1/3
  • None of these
The function f(x) = e-|x| is
  • continuous everywhere but not differentiable at x = 0
  • continuous and differentiable everywhere
  • not continuous at x = 0
  • None of the above
The f(x) is differentiable at x = 1 and
Maths-Limits Continuity and Differentiability-34966.png
  • 8
  • 5
  • 4
  • 3
At x = 0, the function f(x) = e-|x| is
  • continuous but not differentiable
  • discontinuous and differentiable
  • discontinuous and not differentiable
  • continous and differentiable
0:0:1


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