Recent questions tagged easy

Differentiate w.r.t. $x$ the function in $ (3x^2 - 9x + 5)^9 $

asked Nov 21, 2012 by thanvigandhi_1

1 answer

Examine the applicability of Mean Value Theorem for all three functions given in $(i)\;f (x) = [x] \;for\; x \: \in [5,9]$

asked Nov 21, 2012 by thanvigandhi_1

1 answer

Verify Mean Value Theorem, if $ f (x) = x^2 - 4x - 3 $ in the interval $ [a,b]$, where $ a = 1 $ and $b = 4 $.

asked Nov 21, 2012 by thanvigandhi_1

1 answer

Verify Rolle's theorem for the function $ f (x) =x^2 + 2x - 8, x \: \in [ -4 , 2 ]. $

asked Nov 20, 2012 by thanvigandhi_1

1 answer

Consider the binary operation $ \wedge$ on the set $\{1, 2, 3, 4, 5\}$ defined by $a \wedge b = min \{a, b\}$. Write the multiplication table of the operation $ \wedge$ .

asked Nov 20, 2012 by vaishali.a

1 answer

If $ e^y ( x + 1 ) = 1$, show that $ \large\frac{d^2y}{dx^2} = \left(\frac{dy}{dx}\right)^2$

asked Nov 20, 2012 by thanvigandhi_1

1 answer

If $ y = 500e^{\large 7x} + 600e^{\large -7x}$, show that $ \large\frac{d^2y}{dx^2}\normalsize = 49y$

asked Nov 20, 2012 by thanvigandhi_1

1 answer

If $ y = Ae^{mx} + Be^{nx}$, show that $ \large\frac{d^2y}{dx^2} -\normalsize ( m + n ) \large\frac{dy}{dx} +\normalsize mny = 0 $

asked Nov 20, 2012 by thanvigandhi_1

1 answer

If $ y = 3 \cos \: (\log x ) + 4 \sin ( \log x )$, show that $x^2y_2 + xy_1 + y = 0$

asked Nov 20, 2012 by thanvigandhi_1

1 answer

If $ y = 5 \cos x - 3 \sin x $ , prove that $ \large\frac{d^2y}{dx^2}\normalsize + y = 0$

asked Nov 20, 2012 by thanvigandhi_1

1 answer

Find the second order derivatives of the functions given in $ \sin (\log x) $

asked Nov 20, 2012 by thanvigandhi_1

1 answer

Find the second order derivatives of the functions given in $\log ( \log x) $

asked Nov 20, 2012 by thanvigandhi_1

1 answer

Find the second order derivatives of the functions given in $ \tan^{-1} x $

asked Nov 20, 2012 by thanvigandhi_1

1 answer

Find the second order derivatives of $ e^{6x} \cos 3x$

asked Nov 20, 2012 by thanvigandhi_1

1 answer

Find the second order derivatives of the functions given in $ x^3 \log x $

asked Nov 20, 2012 by thanvigandhi_1

1 answer

Find the second order derivatives of the functions given in $\log x $

asked Nov 20, 2012 by thanvigandhi_1

1 answer

Find the second order derivatives of the functions given in $ x \; \cos x$

asked Nov 20, 2012 by thanvigandhi_1

1 answer

Find the second order derivatives of the functions given in $ x^{\large 20} $

asked Nov 20, 2012 by thanvigandhi_1

1 answer

Find the second order derivatives of the functions given in $ x^2 + 3x + 2 $

asked Nov 20, 2012 by thanvigandhi_1

1 answer

If $x$ and $y$ are connected parametrically by the equations given in $ x = a ( \cos \theta + \theta \sin \theta), y = a ( \sin \theta - \theta \cos \: \theta) $ without eliminating the parameter, Find $\frac{\large dy}{\large dx}$.

asked Nov 20, 2012 by thanvigandhi_1

1 answer

If $x$ and $y$ are connected parametrically by the equations given in $x = a \sec \theta, y = b \tan \theta $ without eliminating the parameter, Find $\frac{\large dy}{\large dx}$.

asked Nov 20, 2012 by thanvigandhi_1

1 answer

If $x$ and $y$ are connected parametrically by the equations given in $x = a ( \theta - \sin \theta ), y = a ( 1 +\cos \theta) $ without eliminating the parameter, Find $\large\frac{dy}{dx}$

asked Nov 20, 2012 by thanvigandhi_1

1 answer

Determine whether or not each of the definition of $\ast$ given below gives a binary operation. In the event that $\ast$ is not a binary operation, give justification for this - On$ \; Z^+,\,$ defined $\,$ by$\; ab= a-b $

asked Nov 19, 2012 by vaishali.a

1 answer

If $x$ and $y$ are connected parametrically by the equations given in $ x = \cos \theta -\ cos 2\theta, y = \sin \theta -\ sin 2\theta $ without eliminating the parameter, Find $\large\frac{dy}{dx}$

asked Nov 19, 2012 by thanvigandhi_1

1 answer

If $x$ and $y$ are connected parametrically by the equations given in $x = 4t, \: y = \large\frac{4}{t} $ without eliminating the parameter, Find $\large\frac{dy}{dx}$

asked Nov 19, 2012 by thanvigandhi_1

1 answer

If $x$ and $y$ are connected parametrically by the equations given in $ x = \sin t, y = \cos 2t $ without eliminating the parameter, Find $\large\frac{dy}{dx}$

asked Nov 19, 2012 by thanvigandhi_1

1 answer

If $x$ and $y$ are connected parametrically by the equations given in $ x = a \cos \theta, y = b \cos \theta $ without eliminating the parameter, Find $\frac{\large dy}{\large dx}$

asked Nov 19, 2012 by thanvigandhi_1

1 answer

If $x$ and $y$ are connected parametrically by the equations given in $ x = 2at^2, \: y = at^4 $ without eliminating the parameter, Find $\frac{\large dy}{\large dx}$

asked Nov 17, 2012 by thanvigandhi_1

1 answer

Differentiate $ (x^2 - 5x + 8) (x^3 + 7x + 9 ) $ in three ways mentioned below:\begin{array}{1 1} (i)\;by\;using\;product\;rule & \;\\(ii)\;by\;expanding\;the\;product\;to\;obtain\;a\;single\;polynomial. & \;\\ (iii)\;by\;logarithmic\;differentiation. & \;\end{array} Do they all give the same answer?

asked Nov 17, 2012 by thanvigandhi_1

1 answer

Find the derivative of the function given by $f(x) =( 1 + x )( 1 + x^2) ( 1 + x^4) ( 1 + x^8)$ and hence find $ f' (1).$

asked Nov 17, 2012 by thanvigandhi_1

1 answer

Find $\large\frac{dy}{dx}$ of the functions given in $ y^{\large x} = x^{\large y} $

asked Nov 17, 2012 by thanvigandhi_1

1 answer

Let $f : X \to Y$ be an invertible function. Show that the inverse of $f^{-1}$ is $f$, i.e., $(f^{-1})^{-1} = f$.

asked Nov 16, 2012 by vaishali.a

1 answer

Differentiate the functions given in w.r.t. $x : $ $ (x + 3)^2 \: . \: (x + 4)^3 \: . \: (x + 5)^4 $

asked Nov 16, 2012 by thanvigandhi_1

1 answer

Differentiate the functions given in w.r.t. $x : $ $ x^{\large x} - 2^{\large sin \: x} $

asked Nov 16, 2012 by thanvigandhi_1

1 answer

Differentiate the functions given in w.r.t. $x : $ $ ( \log \; x )^{\large cos \: x} $

asked Nov 16, 2012 by thanvigandhi_1

1 answer

Differentiate the functions given in w.r.t. $x :$ $ \sqrt {\large\frac{(x-1)(x-2)}{(x-3)(x-4)(x-5)}} $

asked Nov 16, 2012 by thanvigandhi_1

1 answer

Differentiate the functions given in w.r.t. $x : $ $ \cos \: x \: . \cos \: 2x \:. \cos \: 3x $

asked Nov 16, 2012 by thanvigandhi_1

1 answer

Differentiate the following w.r.t. $ x: $ $ cos \: ( log\: x + e^x ), x > 0 $

asked Nov 16, 2012 by thanvigandhi_1

1 answer

Differentiate the following w.r.t. $x: \large \frac {\cos x}{\log x}$,$\; x > 0 $

asked Nov 16, 2012 by thanvigandhi_1

1 answer

Differentiate the following w.r.t. $x :$$ log ( log \: x ), x > 1 $

asked Nov 16, 2012 by thanvigandhi_1

1 answer

Differentiate the following w.r.t. $x : \sqrt {e^\sqrt x}, x > 0 $

asked Nov 16, 2012 by thanvigandhi_1

1 answer

Differentiate the following w.r.t. $x : e^x + e^{x^2} + \: ... + e^{x^5} $

asked Nov 16, 2012 by thanvigandhi_1

1 answer

Differentiate the following w.r.t. $x : \log\;( cos \: e^x ) $

asked Nov 16, 2012 by thanvigandhi_1

1 answer

Differentiate the following w.r.t. $x : sin\;( tan^{-1} e^{-x}) $

asked Nov 16, 2012 by thanvigandhi_1

1 answer

The volume of a cube is increasing at the rate of $ 8\;cm^ 3/s$ . How fast is the volume of a cube is increasing at the rate of $8\;cm^ 3 /s$ . How fast is the surface area increasing when the length of an edge is $12 cm$?

asked Nov 16, 2012 by kasturi.c

1 answer

Find the rate of change of the area of a circle with respect to its radius r when $(a)\; r = 3 cm$

asked Nov 16, 2012 by kasturi.c

1 answer

Differentiate the following w.r.t. $x : e^{x^{3} } $

asked Nov 16, 2012 by thanvigandhi_1

1 answer

Differentiate the following w.r.t. $x : e^{sin^{-1} x} $

asked Nov 16, 2012 by thanvigandhi_1

1 answer

Differentiate the following w.r.t. $x : \large \frac{e^x}{sin\;x}$

asked Nov 16, 2012 by thanvigandhi_1

1 answer

Find $\large \frac {dy}{dx} $ in the following: $ y = sec^{-1} \left(\large\frac{1}{2x^2 - 1}\right), 0 < x < \; { \frac{1}{\sqrt2} } \\ $

asked Nov 16, 2012 by thanvigandhi_1

1 answer

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