Recent questions tagged ch5

In onion the swollen underground structure is :-

asked May 5, 2014 by sreemathi.v

1 answer

Broad past of leaf is

asked May 5, 2014 by sreemathi.v

1 answer

Shoot/stem develops from :-

asked May 5, 2014 by sreemathi.v

1 answer

Roots developing from parts of plant other than the radical are :-

asked May 5, 2014 by sreemathi.v

1 answer

Find points on the curve $y=x^2+1$ at which the slope of the tangent is equal to its $x$ coordinate.

asked May 1, 2014 by meena.p

0 answers

Find the equation of normal to the curve $x^2+2y=8x-2 $ at the point $(6,5)$

asked May 1, 2014 by meena.p

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Find the equation of the tangent to the curve $\sqrt x +\sqrt y =a $ at the point $\bigg( \large\frac{a^2}{4},\frac{a^2}{4} \bigg)$

asked May 1, 2014 by meena.p

0 answers

Find the slope of the tangent to the curve $x^2+y^2=4x-2$at the point (3,1)

asked May 1, 2014 by meena.p

1 answer

Verify Mean value theorem for the following functions: $(a)\;f(x)=x(x+4)^2\;on\;[0,4]\\ (b)\;f(x)= 2 \sin x +\sin 2x \;on\;[0,\pi] \\ (c)\;f(x)=x^3-2x^2-x+3\;in\;[0,1] \\ (d)\;f(x)=x +\large\frac{1}{x} \normalsize \;on \;[1,3]$

asked May 1, 2014 by meena.p

0 answers

Verify Rolles theorem for the following functions: $(a) \; f(x)=x^2-5x+4\;on \;[0,4]\\ (b) \; f(x)=x(x-1)^2\;on \;[0,1]\\ (c) \; f(x)=x^3-7x^2+16x-12 \;on \;[2,3]\\ (d) \; f(x)=e^x(\sin x- \cos x)\;on \;[\large\frac{\pi}{4},\frac{5 \pi}{4} ] $

asked May 1, 2014 by meena.p

0 answers

If $y= \sqrt {1-x^2}+x \sqrt {1-y^2} =1$ prove that $\large\frac{dy}{dx} =$$(-1) \sqrt {\large\frac{1-y^2}{1-x^2}}$

asked May 1, 2014 by meena.p

0 answers

If $\sqrt{1-x^2}+\sqrt {1-y^2}=a (x-y),$ a being a constant prove that $\large\frac{dy}{dx} =\large\frac{\sqrt {1-y^2}}{\sqrt {1-x^2}}$

asked May 1, 2014 by meena.p

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If $\sin x =y \sin (x+b)$ show that $\large\frac{dy}{dx} =\frac{\sin b}{\sin ^2 (x+b)}$

asked May 1, 2014 by meena.p

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If $x=a(\theta - \sin \theta) \quad ; y= a(1+\cos \theta) $ find $\large\frac{d^2y}{dx^2}$ at $\theta =\large\frac{\pi}{2}$

asked May 1, 2014 by meena.p

1 answer

If $y=[x+\sqrt {x^2+1} ]^m$ show that $(x^2+1)y_2 +x y_1-m^2y=0$

asked May 1, 2014 by meena.p

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If $x^my^n=(x+y)^{m+n}$ show that $\large\frac{dy}{dx}=\frac{y}{x}$

asked May 1, 2014 by meena.p

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Differentiate the following function: $(x \cos x)^x +(x \sin x)^{\Large\frac{1}{x}}$

asked May 1, 2014 by meena.p

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Differentiate the following function: $x^{\large \sin x +\cos x}$

asked May 1, 2014 by meena.p

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Differentiate the following function: $x ^{\large \cos ^{-1}x}$

asked May 1, 2014 by meena.p

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Differentiate the following function: $\tan^{-1} \bigg( \large \frac{\cos x}{1+\sin x} \bigg)$

asked May 1, 2014 by meena.p

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Differentiate the following function: $ \tan ^{-1}( \sqrt{1+x^2}+x)$

asked May 1, 2014 by meena.p

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Show that $f(x) =|x -2| $ is continuous but not derivable at $x=2$

asked May 1, 2014 by meena.p

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The function $f(x)$ is defined as follows : $f(x) = \left\{ \begin{array}{l l} x^2+ax+b & \quad 0 \leq x < 2 \\ 3x+2, & \quad 2 \leq x \leq 4 \\ 2ax+5b & \quad 4 < x \leq 8 \end{array} \right. $ If $f $ is continuous on $[0,8]$ find the values of a and b

asked May 1, 2014 by meena.p

0 answers

Let $f(x) = \left\{ \begin{array}{l l} \frac{1-\cos 4x}{x^2}, & \quad x < 0 \\ a, & \quad x = 0 \\ \frac{\sqrt x)}{(\sqrt {16+\sqrt x})-4} & \quad x < 0 \end{array} \right. $ Find $a$ if $f $ is continuous at $x=0$

asked May 1, 2014 by meena.p

0 answers

If $ f(x) = \left\{ \begin{array}{l l} \large\frac{x^3+x^2-16x+20}{(x-2)^2} & \quad when \quad x \neq 3 \\ k & \quad when \quad x = 2 \end{array} \right. $ and $f(x)$ is continuous at $x=3$ find the value of k.

asked Apr 22, 2014 by meena.p

1 answer

If $ f(x) = \left\{ \begin{array}{l l} \large\frac{|x+2|}{\tan^{-1} (x+2)} & \quad x \neq -2 \\ 2 & \quad x=-2 \end{array} \right. $ then $f(x) $ is

asked Apr 22, 2014 by meena.p

1 answer

If the function $ f(x) = \left\{ \begin{array}{l l} 3ax+b & \quad for \quad x > 1 \\ 11 & \quad for \quad x = 1 \\ 5ax-2b & \quad for \quad x < 1 \end{array} \right. $ is continuous at $x=1$.find the values of a and b .

asked Apr 22, 2014 by meena.p

1 answer

Find the values of K. So that the function $ f(x) = \left\{ \begin{array}{l l} \large\frac{k \cos x}{\pi -2x} & \quad if \quad x \neq \large\frac{\pi}{2} \\ 3 & \quad if \quad x =\large\frac{\pi}{2} \end{array} \right. $ is continuous at $x =\large\frac{\pi}{2}$ .

asked Apr 22, 2014 by meena.p

1 answer

Determine the value of K so that the function. $ f(x) = \left\{ \begin{array}{l l} Kx^2 & \quad if \quad x \leq 2 \\ 3 & \quad if \quad x > 2 \end{array} \right. $ is continuous .

asked Apr 22, 2014 by meena.p

1 answer

Number of solutions of the equation $\;z^{2}+|z|^{2} =0\;$ is

asked Apr 19, 2014 by yamini.v

1 answer

The amplitude of $\; sin \large\frac{\pi}{5} + i\; \normalsize cos (1-\large\frac{\pi}{5})\;$ is

asked Apr 19, 2014 by yamini.v

1 answer

The equation $\;|z+1-i|=|z-1+i|\;$ represents a

asked Apr 19, 2014 by yamini.v

1 answer