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11th Business Maths Weekly Test - 1 ( Differential Calculus )

MABS Institution

11th Business Maths Weekly Test - 1 ( Differential Calculus )-Aug 2020

Time : 1.30 Hours

Part - A

Multiple Choice Question - Answer All Question

\(\frac{d}{dx}(5e^x-2logx)\) is equal to

5e^x - \(\frac{2}{x}\)
5e^x - 2x
5e^x - \(\frac{1}{x}\)
2 logx

The graph of f(x) = e^x is identical to that of

f(x) = a^x, a > 1
f(x) = a^x, a < 1
f(x) = a^x, 0 < a < 1
y = ax +b, a \(\ne\) 0

f(x) = - 5 , for all \(x\epsilon R\), is a

an identity function
modulus function
exponential function
constant function

\(\frac{d}{dx}(a^x)=\)

\(\frac { 1 }{ x\log { \begin{matrix} a \\ e \end{matrix} } } \)
a^a
\(x\log { \begin{matrix} a \\ e \end{matrix} } \)
\({ a }^{ x }\log { \begin{matrix} a \\ e \end{matrix} } \)

\(\lim _{ x\rightarrow \infty }{ \frac { \tan { \theta } }{ \theta } } =\)

1
\(\infty\)
\(-\infty\)
\(\theta\)

The graph of y = 2x² is passing through

(0,0)
(2,1)
(2,0)
(0,2)

If y = x and z = \(\frac{1}{x}\) then \(\frac{dy}{dz}=\)

x²
1
-x²
\(-\frac{1}{x^2}\)

If f(x) = 2x and get g(x) = \(\frac{1}{2^x}\) then (fg)(x) is

1
0
4^x
\(\frac{1}{4^x}\)

The range of f(x) = |x|, for all \(x\epsilon R\), is

(0, \(\infty \))
(0, \(\infty \))
(-\(\infty \), \(\infty \))
(1, \(\infty \))

\(\lim _{ x\rightarrow 0 }{ \frac { { e }^{ x }-1 }{ x } } =\)

e
nx^(n-1)
1
0

Part - B

Generic 2 - Answer All Question

If \(f(x)={ x }^{ 3 }-\frac { 1 }{ { x }^{ 3 } } \) then show that \(f(x)+f\left( \frac { 1 }{ x } \right) =0\)

Differentiate \({ x }^{ \frac { 2 }{ 3 } }\) from first principles

Differentiate the following functions with respect to x, \(x^{\frac{3}{2}}\)
Differentiate the following functions with respect to x, sin³ x

Evaluate: \(\underset { x\rightarrow \infty }{ lim } x\tan { \left( \frac { 1 }{ x } \right) } \)

Part - C

Generic 3 - Answer All Question

Find \(\frac{dy}{dx}\) of the following functions: x=acos³θ, y=asin³θ

Differentiate the following with respect to x. \(\left( \sqrt { x } +\frac { 1 }{ \sqrt { x } } \right) ^{ 2 }\)

Differentiate the following with respect to x.
(sin x )^{tan x}

Differentiate the following with respect to x.
(sin x)^x
If sin y = x sin(a + y), then prove that \(\frac{dy}{dx}=\frac{sin^2(a+y)}{sin\ a}\).

Part - D

Generic 5 - Answer All Question

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

Draw the graph of the function f(x) = x² - 5.

Find the derivate of (x³-27)from first principles.

Darw the graph of f(x) = log_ax; x > 0, a > 0 and \(a\ne 1\).
Show that f(x) = x² differentiable at x = 1 and find f'(1).

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