Recent questions tagged sec-b

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 $u,\: v$ and $w$ are functions of $x$, then show that $\large\frac{d}{dx} $$( u.v.w) =\large \frac{du}{dx} $$v.w + u . \large\frac{dv}{dx} $$. w + u.v. \large\frac{dw}{dx} $ in two ways - first by repeated application of product rule, second by logarithmic differentiation.

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

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 + 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. $x :$ $ \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

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

asked Nov 15, 2012 by thanvigandhi_1

1 answer

Consider $f:R_+ \to [\;\text{–5}, \infty )$given by $f(x)=9x^2 +6x$-$5$.Show that $f$ is invertible with $ f^{-1} (y) = \bigg(\frac{(\sqrt{y+6}) -1} { 3}\bigg) $

asked Nov 15, 2012 by vaishali.a

1 answer

Consider $ f:R_+ \to [4,\infty)$given by $f(x)=x^2 +4$. Show that $f$ is invertible with the inverse $f^{-1}$of $f$ given by $f^{-1}(y) = \sqrt {y-4}$,where $R_+$ is the set of all non-negative real numbers.

asked Nov 14, 2012 by vaishali.a

1 answer

Consider $f:R \to R$ given by $f(x)=4x+3$. Show that $f$ is invertible. Find the inverse of $ f$

asked Nov 14, 2012 by vaishali.a

1 answer

Show that $f : [-1,1]$ $ \rightarrow R$, given by $f(x) =\frac {x } { (x+2)}$ is one-one. Find the inverse of of the $f : [-1,1] \rightarrow $ Range $ f$.

asked Nov 14, 2012 by vaishali.a

1 answer

Find $ \frac {dy}{dx} $ in the following: $ sin^2y + cos \: xy = k $

asked Nov 11, 2012 by thanvigandhi_1

1 answer

Find the values of $k$ so that the function $f$ is continuous at the indicated point in $ f(x) = \left\{ \begin{array} {1 1} \large\frac{k\cos x}{\pi - 2x}\normalsize,& \quad { if \; x \neq \large\frac{\pi}{2} }\\ \normalsize 3 ,& \quad { if \; x = \large\frac{\pi}{2} }\\ \end{array} \right. \qquad at \; x = \; \large\frac{\pi}{2} $

asked Nov 11, 2012 by thanvigandhi_1

1 answer

Find the values of $a$ and $b$ such that the function defined by $ f(x) = \left\{ \begin{array} {1 1} 5 ,& \quad\text{ if $ x $ $\leq 2$}\\ ax+b,& \quad \text{if $2$ < x<10}\\ 21,& \quad \text{if $ x $ $\geq 10$}\\ \end{array} \right.$ is a continuous function.

asked Nov 11, 2012 by thanvigandhi_1

1 answer

Find the values of $k$ so that the function $f$ is continuous at the indicated point in $ f(x) = \left\{ \begin{array} {1 1} kx+1 ,& \quad\text{ if $ x $ $\leq 5$}\\ 3x-5,& \quad \text{if $x$ > 5}\\ \end{array} \right.\qquad at \; x = 5 $

asked Nov 11, 2012 by thanvigandhi_1

1 answer

Find the values of $k$ so that the function $f$ is continuous at the indicated point in $ f(x) = \left\{ \begin{array} {1 1} kx^2 ,& \quad\text{ if $ x $ $\leq 2$}\\ 3,& \quad \text{if $x$ > 2}\\ \end{array} \right. \qquad at \;x = 2 $

asked Nov 11, 2012 by thanvigandhi_1

1 answer

Examine the continuity of $f$, where $f$ is defined by $ f(x) = \left\{ \begin{array} {1 1} \sin x - \cos x,& \quad\text{ if $x$ $\neq$ 0 }\\ -1 ,& \quad \text{if $x$ =0}\\ \end{array} \right. $

asked Nov 10, 2012 by thanvigandhi_1

1 answer

Find all points of discontinuity of $f$, where $ f(x) = \left\{ \begin{array} {1 1} \large\frac {sinx} {x},\normalsize & \quad\text{ if $x$ < 0 }\\ x + 1 ,& \quad \text{if $x$ $ \geq 0$}\\ \end{array} \right. $

asked Nov 10, 2012 by thanvigandhi_1

1 answer

Find the relationship between $a$ and $b$ so that the function $f$ defined by $ f(x) = \left\{ \begin{array} {1 1} ax + 1 ,& \quad\text{ if $ x $ $\leq 3$}\\ bx + 3,& \quad \text{if $x$ > 3}\\ \end{array} \right. $ is continuous at $x = 3$.

asked Nov 10, 2012 by thanvigandhi_1

1 answer