Important Questions of Continuity and Differentiability Mathematics | Zigya

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201.

If x = 1 - t21 + t2 and y = 2at1 +t2, then dydx is equal to

  • a1 - t22t

  • at2 - 12t

  • at2 + 12t

  • at2 - 1t


202.

The value of logfx + 23x is

  • log1 + fxfx + 4 . 3x

  • log1 + fxfx + 3x

  • logfx1 + fx + 4 . 3x

  • logfx1 + fx + 3x


203.

If x2y5 = (x + y)7, then d2ydx2 is equal to

  • y/x2

  • x/y

  • 1

  • 0


204.

If x = x = secθ, y = tanθ, then the value of d2ydx2 at θ = π4 is

  • 0

  • 1

  • - 1

  • 2


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205.

 If x = f(t) and y =g(t), then the value of d2ydx2 is

  • f'tg''t - g'tf''tf't3

  • f'tg''t - g'tf''tf't2

  • 'tf''t - g''tf'tf't2

  • g'tf''t - g''tf'tf't3


206.

The value of a and b such that the function

fx = - 2sinx,      - π  x  - π2asinx + b,     - π2 < x < π2cosx,                   π2  x  π

is continuous in - π, π, are

  • - 1, 0

  • 1, 0

  • 1, 1

  • - 1, 1


207.

If g is the inverse of f and f'(x) = 11 + x2, then g'(x) is equal to

  • 1 + [g(x)]2

  • - 11 + [g(x)]2

  • 121 + x2

  • None of these


208.

If f(x) = 1 + sinxasinx, - π6 < x < 0etan2xtan3x,                        0 < x < π6 is continuous at x = 0, find the values of a and b.

  • 3/2, e3/2

  • - 2/3, e- 3/2

  • 2/3, e2/3

  • None of these


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209.

If f(x) = exg(x), g(0) = 2, g'(0) = 1 then f'(0) is

  • 1

  • 3

  • 2

  • 0


210.

At the point x = 1, the function

fx = x3 - 1,    1 < x < x - 1, -  < x  1

  • continuous and differentiable

  • continuous and not differentiable

  • discontinuous and differentiable

  • discontinuous and not differentiable


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