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In many books a shortcut trick for checking differnetiabiltiy of a fuction is given by first differentiate LHS and RhS and check if both the slope are coming same, provided the function is continous. However in many question ...
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if f(x - 1) + f(x + 1) = √3 f(x) then prove that f(x) is periodic with period 12` ...
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1) ∫√secx ...
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\hspace{-16}\bf{\int\tan^{2}(x).\sin^{-1}(\tan x-x)dx} ...
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Please integrate ∫(x^2 + 1)/(x^4+x^2+1) dx ...
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my question is in solving a equation say f(x)=g(x) graphically if it happens that I am confused that whether the graph of f(x) really intersects a point or not ...how to get rid of that confusion?? ...
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Show that infinete series Σ sin( 1/k ) is div? ...
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\hspace{-16}\mathbb{I}$f $\bf{n=\frac{1}{\frac{1}{1980}+\frac{1}{1981}+........+\frac{1}{2012}}}$. Then $\bf{\lfloor n \rfloor}$ is \\\\\\ Where $\bf{\lfloor x \rfloor = }$Floor Sum. ...
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*Image* ...
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What will be the graph of (Sinx)/x ? ...
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What will be the graph of (Sinx)/x ? ...
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∫√x+√x2+2.dx plz help me out to solve dis one ...
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\hspace{-16}\bf{\left\lfloor \dfrac{10^{20000}}{3+10^{100}}\right\rfloor=}$\\\\\\ Where $\bf{\lfloor x \rfloor =}$ Floor Function. ...
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\hspace{-16}$If $\bf{f:(0,\infty)\rightarrow (1,\infty)}$ and $\bf{f(x)=x^4+x^2+x+1}$. Then $\bf{\frac{d}{dx}\left\{f^{-1}(4)\right\}=}$ ...
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\hspace{-16}$If $\bf{\mathbb{I} = \int_{0}^{\pi}\frac{\pi}{\pi^2-\cos^2 (x)}dx}$, Then $\bf{[\;\mathbb{I}\; ]=}$ ...
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*Image* ...
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\hspace{-16}$If $\bf{f(x+1)=(-1)^{x+1}.x-2f(x)\forall x\in \mathbb{N}}$ and $\bf{f(1)=f(1986)}$\\\\ Then Sum of Digit of the no. $\bf{f(1)+f(2)+f(3)+.....+f(1985)}$ ...
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\hspace{-16}$If $\bf{\mathbb{I}=\int_{0}^{\pi}\frac{\sin(884\;x).\sin(1122\;x)}{\sin (x)}dx}$ and $\bf{\mathbb{J}=\int_{0}^{1}\frac{x^{238}.(x^{1768}-1)}{(x^2-1)}dx}$\\\\\\ Then value of $\bf{\frac{\mathbb{I}}{\mathbb{J}}=}$ ...
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I=∫ 6x3+x2-2x+1/2x-1 . Integrate this function. ...
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\hspace{-16}\bf{\mathbb{S}}$olve for $\bf{x}$\\\\ $\bf{(1)\;\; \lfloor 1.5 \rfloor x+\lfloor x \rfloor=5}$\\\\ $\bf{(2)\;\; \lfloor x \rfloor+\lfloor 2x \rfloor \leq \sqrt{3}}$ ...
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\hspace{-16}\bf{\mathbb{F}}$ind a function $\bf{f:\mathbb{R}\rightarrow \mathbb{R}}$ that satisfy\\\\\\ $\bf{2f(x)+f(-x)=\left\{\begin{matrix} \bf{-x^3-3}\;\;\;,\;x\leq 1\\\\ \bf{7-x^3}\;\;\;,\;x> 1 \end{matrix}\right.}$ ...
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Given: f(x) =ax2+bx+c g(x)= px2+qx+r such that f(1)=g(1), f(2)=g(2) and f(3)-g(3) = 2 . Find f(4)-g(4). The q is easy but i want a shorter method... ...
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\hspace{-16}\bf{\int_{0}^{\frac{\pi}{4}}\ln \left(\frac{1+\sin^2 2x}{\sin^4 x+\cos^4 x}\right)dx} ...
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\hspace{-16}\bf{\int_{-1}^{1}\frac{2x^{1004}+x^{3014}+x^{2008}.\sin(x)^{2007}}{1+x^{2010}}dx} ...
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Find ∫ ( 1/x6 + 1/x8 )1/3dx i.e integrate cubic root of (1/x6+1/x8) ...
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\hspace{-16}\bf{\int_{0}^{4\pi}\ln\left|13.\sin (x)+3\sqrt{3}.\cos (x)\right|dx}= ...
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1) tan3x +cos (2.5x) 2) cos(cosx) + cos(sinx) ...
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\hspace{-16}\bf{\int_{\frac{25\pi}{4}}^{\frac{53\pi}{4}}\frac{1}{(1+2^{\sin x}).(1+2^{\cos x})}dx} ...
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\hspace{-16}\bf{\lim_{n\rightarrow \infty}\sum_{i=0}^{n}\;\sum_{j=0}^{n-i}\frac{x^j}{i!\;.\;j!}=} ...
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\hspace{-16}\bf{\int\frac{x^2.\cos^{-1}\big(x\sqrt{x}\big)}{\big(1-x^3\big)^2}dx} ...
repliedJun 12 '12 at 23:11
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repliedMay 27 '12 at 20:02
askedMay 22 '12 at 1:41
repliedFeb 23 '13 at 11:05
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repliedMay 14 '12 at 22:33
repliedMay 2 '12 at 21:56
repliedMay 8 '12 at 5:21