Recent questions tagged bookproblem

Find the absolute maximum and minimum values of the function $(f)$ given by $ f (x) = cos^2 x + sin\: x, x\: \in [0, \pi]$

asked Nov 28, 2012 by thanvigandhi_1

1 answer

Find the points at which the function $f$ given by $f (x) = (x – 2)^4 (x + 1)^3$ has a (i) local maxima, (ii) local minima and the (iii) point of inflexion.

asked Nov 28, 2012 by thanvigandhi_1

1 answer

A point on the hypotenuse of a triangle is at distance $a$ and $b$ from the sides of the triangle.Show that the maximum length of the hypotenuse is $ (a^{\large\frac{2}{3}} + $$b^{\large\frac{2}{3}})^{\Large\frac{3}{2}}$

asked Nov 28, 2012 by thanvigandhi_1

1 answer

A window is in the form of a rectangle surmounted by a semicircular opening. The total perimeter of the window is 10 m. Find the dimensions of the window to admit maximum light through the whole opening.

asked Nov 28, 2012 by thanvigandhi_1

1 answer

The sum of the perimeter of a circle and square is $k$, where $k$ is some constant. Prove that the sum of their areas is least when the side of square is double the radius of the circle.

asked Nov 28, 2012 by thanvigandhi_1

1 answer

A tank with rectangular base and rectangular sides, open at the top is to be constructed so that its depth is $2 m$ and volume is $8 m^3$. If building of tank costs Rs 70 per sq metres for the base and Rs 45 per square metre for sides. What is the cost of least expensive tank?

asked Nov 28, 2012 by thanvigandhi_1

1 answer

Find the maximum area of an isosceles triangle inscribed in the ellipse $\large\frac{x^2}{a^2} + \frac{y^2}{b^2} $$= 1 $ with its vertex at one end of the major axis.

asked Nov 28, 2012 by thanvigandhi_1

2 answers

Find the intervals in which the function $f$ given by $f(x) = x^3 + \large\frac{1}{x^3}$$, x \neq 0$ is $(i) \;increasing\qquad (ii) \;decreasing.$

asked Nov 28, 2012 by thanvigandhi_1

1 answer

Find the intervals in which the function $f$ given by $ f(x) =\large \frac{4sin\: x - 2x - xcos \: x}{2+cos\:x}$ is (i) increasing (ii) decreasing.

asked Nov 28, 2012 by thanvigandhi_1

1 answer

Show that the normal at any point $\theta$ to the curve $ x = a \cos\theta + a \: \theta \sin\: \theta, y = a\sin\theta - a\theta \cos\theta$ is at a constant distance from the origin.

asked Nov 28, 2012 by thanvigandhi_1

1 answer

Find the equation of the normal to curve $y^2 = 4x$ which passes through the point $(1, 2).$

asked Nov 28, 2012 by thanvigandhi_1

1 answer

The two equal sides of an isosceles triangle with fixed base $b$ are decreasing at the rate of 3 cm per second. How fast is the area decreasing when the two equal sides are equal to the base ?

asked Nov 28, 2012 by thanvigandhi_1

1 answer

Show that the function given by $ f(x) =\large \frac{\log \: x}{x}$ has maximum at $x = e.$

asked Nov 28, 2012 by thanvigandhi_1

1 answer

Using differentials, find the approximate value of each of the following: $(33)^{-\large\frac{1}{5}}$

asked Nov 28, 2012 by thanvigandhi_1

1 answer

Using differentials, find the approximate value of each of the following: $ \left(\large\frac{17}{81}\right)^{\frac{1}{4}}$

asked Nov 28, 2012 by thanvigandhi_1

1 answer

Determine order and degree (if defined) of differential equation $y'+5y=0$

asked Nov 28, 2012 by sreemathi.v

1 answer

Determine order and degree (if defined) of differential equation $(y''')^2+(y'')^3+(y')^4+y^5=0$

asked Nov 27, 2012 by sreemathi.v

1 answer