11th Business Maths Weekly Test -2 ( Differential Calculus )

MABS Institution

11th Business Maths Weekly Test -2 ( Differential Calculus )-Aug 2020

Time : 1.30 Hours

Part - A

Generic 2 - Answer All Question

Find the domain for which the functions f(x) = 2x² - 1 and g(x) = 1 - 3x are equal.

Differentiate \(\frac { { x }^{ 2 }cos\frac { \pi }{ 4 } }{ sinx } \)

If f(x) = x and and g(x) = |x|, then find (f - g)(x)

If x³ + y³ = 3axy, then find \(\frac{dy}{dx}\).

Evaluate: \(\underset { x\rightarrow 0 }{ lim } \frac { \sin { 3x } }{ \sin { 5x } } \)

Determine whether the following functions are odd or even?
f(x)=x+x²

Find \(\frac { dy }{ dx } \) if x² + xy + y² = 100

Determine whether the following functions are odd or even?
f(x) = sin x +cos x

Evaluate: \(\underset { x\rightarrow 1 }{ lim } \left( { 3x }^{ 2 }+4x-5 \right) \)

Evaluate: \(\underset { x\rightarrow 2 }{ lim } \frac { { x }^{ 2 }-4x+6 }{ x+2 } \)

Part - B

Generic 5 - Answer All Question

If \(y={ \left( x+\sqrt { 1+{ x }^{ 2 } } \right) }^{ m }\) , then show that (1 + x)² y₂ + xy₁ - m² = 0.

Show that the function f(x) = |x| is not differentiable at x = 0.

Draw the graph of the following function f(x)=e^2x
Evaluate \(\begin{matrix} \underset { x\rightarrow 1 }{ lim } & \frac { { x }^{ 7 }-2{ x }^{ 5 }+1 }{ { x }^{ 3 }-{ 3x }^{ 2 }+2 } \end{matrix}\)

A group of students wish to charter a bus for an educational tour which can accommodate atmost 50 students. The bus company requires at least 35 students for that trip. The bus company charges Rs 200 per student up to the strength of 45. For more than 45 students, company charges each student Rs 200 less \(\frac{1}{5}\) times the number more than 45. Consider the number of students who participates the tour as a function, find the total cost and its domain.

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11th Business Maths Weekly Test -2 ( Differential Calculus )

MABS Institution

11th Business Maths Weekly Test -2 ( Differential Calculus )-Aug 2020

Part - A

Generic 2 - Answer All Question

Find the domain for which the functions f(x) = 2x2 - 1 and g(x) = 1 - 3x are equal.

Differentiate \(\frac { { x }^{ 2 }cos\frac { \pi }{ 4 } }{ sinx } \)

If f(x) = x and and g(x) = |x|, then find (f - g)(x)

If x3 + y3 = 3axy, then find \(\frac{dy}{dx}\).

Evaluate: \(\underset { x\rightarrow 0 }{ lim } \frac { \sin { 3x } }{ \sin { 5x } } \)

Determine whether the following functions are odd or even? f(x)=x+x2

Find \(\frac { dy }{ dx } \) if x2 + xy + y2 = 100

Determine whether the following functions are odd or even? f(x) = sin x +cos x

Evaluate: \(\underset { x\rightarrow 1 }{ lim } \left( { 3x }^{ 2 }+4x-5 \right) \)

Evaluate: \(\underset { x\rightarrow 2 }{ lim } \frac { { x }^{ 2 }-4x+6 }{ x+2 } \)

Part - B

Generic 5 - Answer All Question

If \(y={ \left( x+\sqrt { 1+{ x }^{ 2 } } \right) }^{ m }\) , then show that (1 + x)2 y2 + xy1 - m2 = 0.

Show that the function f(x) = |x| is not differentiable at x = 0.

Draw the graph of the following function f(x)=e2x

Evaluate \(\begin{matrix} \underset { x\rightarrow 1 }{ lim } & \frac { { x }^{ 7 }-2{ x }^{ 5 }+1 }{ { x }^{ 3 }-{ 3x }^{ 2 }+2 } \end{matrix}\)

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Find the domain for which the functions f(x) = 2x² - 1 and g(x) = 1 - 3x are equal.

If x³ + y³ = 3axy, then find \(\frac{dy}{dx}\).

Determine whether the following functions are odd or even?
f(x)=x+x²

Find \(\frac { dy }{ dx } \) if x² + xy + y² = 100

Determine whether the following functions are odd or even?
f(x) = sin x +cos x

If \(y={ \left( x+\sqrt { 1+{ x }^{ 2 } } \right) }^{ m }\) , then show that (1 + x)² y₂ + xy₁ - m² = 0.

Draw the graph of the following function f(x)=e^2x