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Recent questions tagged p178

The area of the region bounded by the curve $x=2y+3$ and the y-lines $y=1$ and $y=-1$ is \[(A)\;4 sq.units\quad(B)\;\frac{3}{2} sq. units\quad(C)\;6 sq.units\quad(D)8 sq.units\]

asked Jan 16, 2013 by sreemathi.v

1 answer

The area of the region bounded by the curve $y=x+1$ and the lines $x=2$ and $x=3$ is \[(A)\frac{7}{2} sq.units\quad(B)\;\frac{9}{2}sq. units\quad(C)\frac{11} {2}sq.units\quad(D)\frac{13}{2} sq.units\]

asked Jan 16, 2013 by sreemathi.v

1 answer

The area of the region bounded by the circle $x^2+y^2=1$ is \[(A)\;2\pi sq.units\quad(B)\;\pi sq. units\quad(C)\;3\pi sq.units\quad(D)4\pi sq.units\]

asked Jan 16, 2013 by sreemathi.v

1 answer

The area of the region bounded by the ellipse $\large\frac{x^2}{25}+\frac{y^2}{16}=1$ is \begin{array}{1 1}(A)\;2 \pi sq.units & (B)\;20{\pi}^2 sq.units\\(C)\;16{\pi}^2 sq.units & (D)\;25\pi sq.units \end{array}

asked Jan 16, 2013 by sreemathi.v

1 answer

The area of the region bounded by the curve $y=sin x$ between the ordinates $x=0$ and $x=\large\frac{\pi}{2}$ and the x-axis is

asked Jan 16, 2013 by sreemathi.v

1 answer

The area of the region bounded by parabola $y^2=x$ and the straight line $2y=x$ is \begin{array}{1 1}(A)\;\frac{4}{3} sq.units & (B)\;1 sq.units\\(C)\;\frac{2}{3} sq.units & (D)\;\frac{1}{3}sq.units \end{array}

asked Jan 16, 2013 by sreemathi.v

1 answer

The area of the region bounded by the curve $y=\cos x$ between $x=0$ and $x=\pi$ is \begin{array}{1 1}(A)\;2 sq.units & (B)\;4 sq.units\\(C)\;3 sq.units & (D)\;1sq.units \end{array}

asked Jan 16, 2013 by sreemathi.v

1 answer

The area of the region in the first quadrant enclosed by the x-axis,the line y=x and the circle $x^2+y^2=32$ is \begin{array}{1 1}(A)\;16\pi\; sq.units & (B)\;4\pi \;sq.units\\(C)\;32\pi\; sq.units & (D)\;24\pi\;sq.units \end{array}

asked Jan 16, 2013 by sreemathi.v

2 answers

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 function $xy = e^{\large(x-y)}$

asked Nov 17, 2012 by thanvigandhi_1

1 answer

Find $\large\frac{dy}{dx}$ of the function $(\cos x)^{\large y} = (\cos y)^{\large x}$

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

Find $\large\frac{dy}{dx}$ of the functions given in $ x^{\large y }+ y^{\large x }= 1 $

asked Nov 17, 2012 by thanvigandhi_1

1 answer

Differentiate the functions given in w.r.t. $x : $ $ (x \cos x )^{\large x} + (x\sin x)^{\Large\frac{1}{x}} $

asked Nov 17, 2012 by thanvigandhi_1

1 answer

Differentiate the functions given in w.r.t. $x : $ $ x^{\large x \cos x} + \large\frac{x^2 + 1}{x^2 - 1} $

asked Nov 17, 2012 by thanvigandhi_1

1 answer

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

asked Nov 17, 2012 by thanvigandhi_1

1 answer

Differentiate the functions given in w.r.t. $x$ : $ (\sin x )^{\large x} + \sin^{-1} \sqrt x $

asked Nov 17, 2012 by thanvigandhi_1

1 answer

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

asked Nov 17, 2012 by thanvigandhi_1

1 answer

Differentiate the functions given in w.r.t. $x : $ $ (x + \large\frac{1}{x})^{\large x}$$ + x ^{\large (1 + \Large\frac{1}{x})} $

asked Nov 17, 2012 by thanvigandhi_1

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

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