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

MABS Institution

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

Time : 2.00 Hours

Part - A

Generic 5 - Answer All Question

If \(y={ e }^{ a\cos ^{ -1 }{ x } }\) , show that \(\left( 1-{ x }^{ 2 } \right) \frac { { d }^{ 2 }y }{ { dx }^{ 2 } } -x\frac { dy }{ dx } -{ a }^{ 2 }y=0\)

Show that f(x) = \(\begin{cases} 5x-4,\quad if0 is continous at x = 1

Differentiate sin (tan^-1 (e^-x))

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

Differentiate the following with respect to x.
(i) x^x
(ii) (log x)^{cos x}

Examine the following functions for continuity at indicated points
\(f(x)=\begin{cases} \frac { { x }^{ 2 }-4 }{ x-2 } ,\quad if\quad x\neq 2 \\ \quad \quad \quad 0,\quad \quad if\quad x=2 \end{cases}at\quad x=2\)

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 function f(x) = x² - 5.

If x^m.yⁿ =(x+y)^(m+n) ,then show that \(\frac { dy }{ dx } =\frac { y }{ x } \)

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.

if y = 2 sin x + 3 cos x, then show that y₂ + y = 0

Verify the continuity and differentiability of \(\\ f\left( x \right) =\begin{cases} 1-x\quad \quad \quad \quad \quad if\ x<1 \\ \left( 1-x \right) \left( 2-x \right) \quad if\quad 1\le x\le 2\ at\quad x-1\quad and\quad x=2 \\ 3-x\quad \quad \quad \quad \quad if\quad x>2 \end{cases}\)

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

MABS Institution

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

Part - A

Generic 5 - Answer All Question

If \(y={ e }^{ a\cos ^{ -1 }{ x } }\) , show that \(\left( 1-{ x }^{ 2 } \right) \frac { { d }^{ 2 }y }{ { dx }^{ 2 } } -x\frac { dy }{ dx } -{ a }^{ 2 }y=0\)

Show that f(x) = \(\begin{cases} 5x-4,\quad if0 is continous at x = 1

Differentiate sin (tan-1 (e-x))

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

Differentiate the following with respect to x. (i) xx (ii) (log x)cos x

Examine the following functions for continuity at indicated points \(f(x)=\begin{cases} \frac { { x }^{ 2 }-4 }{ x-2 } ,\quad if\quad x\neq 2 \\ \quad \quad \quad 0,\quad \quad if\quad x=2 \end{cases}at\quad x=2\)

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 function f(x) = x2 - 5.

If xm.yn =(x+y)(m+n) ,then show that \(\frac { dy }{ dx } =\frac { y }{ x } \)

if y = 2 sin x + 3 cos x, then show that y2 + y = 0

Verify the continuity and differentiability of \(\\ f\left( x \right) =\begin{cases} 1-x\quad \quad \quad \quad \quad if\ x<1 \\ \left( 1-x \right) \left( 2-x \right) \quad if\quad 1\le x\le 2\ at\quad x-1\quad and\quad x=2 \\ 3-x\quad \quad \quad \quad \quad if\quad x>2 \end{cases}\)

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Tamilnadu Stateboardszs - Class

Differentiate sin (tan^-1 (e^-x))

Differentiate the following with respect to x.
(i) x^x
(ii) (log x)^{cos x}

Examine the following functions for continuity at indicated points
\(f(x)=\begin{cases} \frac { { x }^{ 2 }-4 }{ x-2 } ,\quad if\quad x\neq 2 \\ \quad \quad \quad 0,\quad \quad if\quad x=2 \end{cases}at\quad x=2\)

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 function f(x) = x² - 5.

If x^m.yⁿ =(x+y)^(m+n) ,then show that \(\frac { dy }{ dx } =\frac { y }{ x } \)

if y = 2 sin x + 3 cos x, then show that y₂ + y = 0