Expansion of log 1 + 3 x + 2 x 2 is

3 x - 5 / 2 x 2 + 9 / 3 x 3 - 17 / 4 x 4 + … … … ∞

3 x - 5 / 4 x 2 + 9 / 3 x 3 - 17 / 4 x 4 + … … … ∞

4 x - 5 / 4 x 2 + 9 / 3 x 3 - 17 / 4 x 4 + … … … ∞

- 3 x - 5 / 2 x 2 - 9 / 3 x 3 - 17 / 4 x 4 + … … …

Let C θ = ∑ n = 0 ∞ cos n θ n ! Which of the following statements is FALSE?

C ′ θ ≠ 0 for all θ ∈ R

If x 2 + y 2 = 1 , then

y y ′ ′ - 2 y ′ 2 + 1 = 0

y y ′ ′ + 2 y ′ 2 + 1 = 0

HARD

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If $f (x) = |\begin{matrix} x^{3} & x^{4} & 3 x^{2} \\ 1 & - 6 & 4 \\ p & p^{2} & p^{3} \end{matrix}|$ , where $p$ is a constant, then $\frac{d^{4} f (x)}{d x^{4}}$ is

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Important Questions on Continuity and Differentiability

EASY

Mathematics>Differential Calculus>Continuity and Differentiability>Second Order Derivative

If $e^{y} (x + 1) = 1$ , then $\frac{d^{2} y}{d x^{2}} =$

HARD

Mathematics>Differential Calculus>Continuity and Differentiability>Second Order Derivative

y = e^{n x}

, then

\frac{d^{2} y}{d x^{2}} . \frac{d^{2} x}{d y^{2}}

is equal to :

HARD

Mathematics>Differential Calculus>Continuity and Differentiability>Second Order Derivative

y^{2} + \log_{e} (\cos^{2} x) = y, x \in (- \frac{π}{2}, \frac{π}{2})

then :

EASY

Mathematics>Differential Calculus>Continuity and Differentiability>Second Order Derivative

y = 2 x^{n + 1} + \frac{3}{x^{n}}

, then

x^{2} \frac{d^{2} y}{d x^{2}}

EASY

Mathematics>Differential Calculus>Continuity and Differentiability>Second Order Derivative

x = A \cos 4 t + B \sin 4 t

,

then

\frac{d^{2} x}{d t^{2}} =

HARD

Mathematics>Differential Calculus>Continuity and Differentiability>Second Order Derivative

a x^{2} + 2 h x y + b y^{2} = 0,

then

\frac{d^{2} y}{d x^{2}} =

EASY

Mathematics>Differential Calculus>Continuity and Differentiability>Second Order Derivative

x = a \sec^{2} θ, y = a \tan^{2} θ

then

\frac{d^{2} y}{d x^{2}} =

HARD

Mathematics>Differential Calculus>Continuity and Differentiability>Second Order Derivative

x = \log t, y + 1 = \frac{1}{t}

, then

e^{- x} \frac{d^{2} x}{d y^{2}} + \frac{d x}{d y} =

MEDIUM

Mathematics>Differential Calculus>Continuity and Differentiability>Second Order Derivative

y = {[x + \sqrt{x^{2} - 1}]}^{15} + {[x - \sqrt{x^{2} - 1}]}^{15}

, then

(x^{2} - 1) \frac{d^{2} y}{d x^{2}} + x \frac{d y}{d x}

is equal to

HARD

Mathematics>Differential Calculus>Continuity and Differentiability>Second Order Derivative

2 x = y^{\frac{1}{5}} + y^{- \frac{1}{5}}

and

(x^{2} - 1) \frac{d^{2} y}{d x^{2}} + λ x \frac{d y}{d x} + k y = 0

, then

λ + k

is equal to

MEDIUM

Mathematics>Differential Calculus>Continuity and Differentiability>Second Order Derivative

y = \frac{{(\sin^{- 1} x)}^{2}}{2}

, then

(1 - x^{2}) y_{2} - x y_{1} =

HARD

Mathematics>Differential Calculus>Continuity and Differentiability>Second Order Derivative

\cos^{- 1} (\frac{y}{b}) = \log (\frac{x}{n}),

then

x^{2} y_{2} + x y_{1} =

EASY

Mathematics>Differential Calculus>Continuity and Differentiability>Second Order Derivative

y = e^{4 x} \cos 5 x,

then

\frac{d^{2} y}{d x^{2}}

x = 0

HARD

Mathematics>Differential Calculus>Continuity and Differentiability>Second Order Derivative

x = e^{t} \sin t

and

y = e^{t} \cos t

t

is a parameter, then the value of

\frac{d^{2} x}{d y^{2}} + \frac{d^{2} y}{d x^{2}}

t = 0,

EASY

Mathematics>Differential Calculus>Continuity and Differentiability>Second Order Derivative

y = 3 e^{5 x} + 5 e^{3 x}

, then

\frac{d^{2} y}{d x^{2}} - 8 \frac{d y}{d x} =

MEDIUM

Mathematics>Differential Calculus>Continuity and Differentiability>Second Order Derivative

Expansion of

\log (1 + 3 x + 2 x^{2})

MEDIUM

Mathematics>Differential Calculus>Continuity and Differentiability>Second Order Derivative

y = a \sin x + (5 + 2 x) \cos x,

then

y^{''} + y =

MEDIUM

Mathematics>Differential Calculus>Continuity and Differentiability>Second Order Derivative

Let

C (θ) = \sum_{n = 0}^{\infty} \frac{\cos (n θ)}{n!}

Which of the following statements is FALSE?

MEDIUM

Mathematics>Differential Calculus>Continuity and Differentiability>Second Order Derivative

x + y = \tan^{- 1} y

and

y^{″} = f (y) y^{'},

then

f (y) =

MEDIUM

Mathematics>Differential Calculus>Continuity and Differentiability>Second Order Derivative

x^{2} + y^{2} = 1

, then

If fx=x3x43x21-64pp2p3 , where p is a constant, then d4fxdx4 is

Important Questions on Continuity and Differentiability

Learn and Prepare for any exam you want !

If $f (x) = |\begin{matrix} x^{3} & x^{4} & 3 x^{2} \\ 1 & - 6 & 4 \\ p & p^{2} & p^{3} \end{matrix}|$ , where $p$ is a constant, then $\frac{d^{4} f (x)}{d x^{4}}$ is