11th Business Maths Weekly Test - 4 ( Differential Calculus )

MABS Institution

11th Business Maths Weekly Test - 4 ( Differential Calculus )-Aug 2020

Time : 1.30 Hours

Part - A

Generic 3 - Answer All Question

If \(y=\sqrt { x } +\frac { 1 }{ \sqrt { x } } \) show that \(2x\frac { dy }{ dx } +y=2\sqrt { x } \).

Find \(\frac { dy }{ dx } \) for the following function x³+y³+3axy=1

If \(f\left( x \right) =\begin{cases} \frac { x-\left| x \right| }{ x } \quad ifx\neq 0 \\ \quad 2\quad \quad ifx=0 \end{cases}\) , then show that \(\underset { x\rightarrow 0 }{ lim } f\left( x \right) \) does not exist.

Find \(\frac { dy }{ dx } \) for the following functions:
xy=tan(xy)

Differentiate: \(\sqrt{\frac{(x-3)(x^2+4)}{3x^2+4x+5}}\)

Differentiate the following with respect to x. sin² x

If x\(\sqrt { 1+y } +y\sqrt { 1+x } =0\) and x≠y, then prove that \(\frac { dy }{ dx } =\frac { -1 }{ (x+1)^{ 2 } } \).

Differentiate the following with respect to x.
sin (x²)

Evaluate the following \(\lim _{ x\rightarrow \infty }{ \frac { 2x+5 }{ { x }^{ 2 }+3x+9 } } \)

If \(\lim _{ x\leftarrow 2 }{ \frac { { x }^{ n }-2^{ n } }{ x-2 } =448 } \) ,then find the least positive integer n

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11th Business Maths Weekly Test - 4 ( Differential Calculus )

MABS Institution

11th Business Maths Weekly Test - 4 ( Differential Calculus )-Aug 2020

Part - A

Generic 3 - Answer All Question

If \(y=\sqrt { x } +\frac { 1 }{ \sqrt { x } } \) show that \(2x\frac { dy }{ dx } +y=2\sqrt { x } \).

Find \(\frac { dy }{ dx } \) for the following function x3+y3+3axy=1

If \(f\left( x \right) =\begin{cases} \frac { x-\left| x \right| }{ x } \quad ifx\neq 0 \\ \quad 2\quad \quad ifx=0 \end{cases}\) , then show that \(\underset { x\rightarrow 0 }{ lim } f\left( x \right) \) does not exist.

Find \(\frac { dy }{ dx } \) for the following functions: xy=tan(xy)

Differentiate: \(\sqrt{\frac{(x-3)(x^2+4)}{3x^2+4x+5}}\)

Differentiate the following with respect to x. sin2 x

If x\(\sqrt { 1+y } +y\sqrt { 1+x } =0\) and x≠y, then prove that \(\frac { dy }{ dx } =\frac { -1 }{ (x+1)^{ 2 } } \).

Differentiate the following with respect to x. sin (x2)

Evaluate the following \(\lim _{ x\rightarrow \infty }{ \frac { 2x+5 }{ { x }^{ 2 }+3x+9 } } \)

If \(\lim _{ x\leftarrow 2 }{ \frac { { x }^{ n }-2^{ n } }{ x-2 } =448 } \) ,then find the least positive integer n

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Tamilnadu Stateboardszs - Class

Find \(\frac { dy }{ dx } \) for the following function x³+y³+3axy=1

Find \(\frac { dy }{ dx } \) for the following functions:
xy=tan(xy)

Differentiate the following with respect to x. sin² x

Differentiate the following with respect to x.
sin (x²)