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\hspace{-16}$How can I calculate Cont. and Diff. of $\bf{f(x) = \lim_{n\rightarrow \infty}\bold{\sqrt[2n]{\bold{\sin^{2n}x+\cos^{2n}x}}}}$ ...
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\hspace{-16}\bf{\lim_{x \rightarrow 0}\frac{1-(1+x)^{\frac{1}{x}}}{x}=} ...
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\hspace{-16}\bf{(1)\; \int\frac{1}{x^4.(x^6+1)}dx}$\\\\\\ $\bf{(2)\;\; \int\frac{2+\sqrt{x}}{(1+x+\sqrt{x})^2}dx}$\\\\\\ $\bf{(3)\;\; \int \left\{1+\tan x.\tan (x+\theta)\right\}dx}$\\\\\\ $\bf{(4)\;\; \int \frac{\sec x.\tan ...
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∫(-100 to 100) [t3]dt ...
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A real valued function f is defined on the interval (-1,2).A point x is said to be a fixed point of f if f(x)=x.Suppose that f is a differentiable function such that f(0)>0 and f(1)=1.Show that if f'(1)>1,then f has a f ...
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What is the derivative of f(x)=x |x| ? ...
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∫(a2-b2 *x2))-3/2 dx ...
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*Image* [x]=Greatest Integer function ...
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lim n ->∞ 1/2n log(2nCn) ...
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∫ tanx ...
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*Image* ...
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\hspace{-16}$If $\bf{f(x)=\frac{x^2}{1+x^2}.}$ Then Determine value of the following expression\\\\\\ $\bf{f\left(\frac{1}{2000}\right)+f\left(\frac{2}{2000}\right)+...+f\left(\frac{1999}{2000}\right)+f\left(\frac{2000}{2000} ...
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Differentiate this ( a+x - a-x )/( a+x + a-x ) ...
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Please give me a hint to solve this problem....... *Image* ...
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\hspace{-16}\bf{(1)\;\;\int \left(\frac{x^2-1}{x^2+1}\right).\frac{1}{\sqrt{x^4+1}}dx}$\\\\\\ $\bf{(2)\;\;\int \left(\frac{x^2+1}{x^2-1}\right).\frac{1}{\sqrt{x^4+1}}dx}$\\\\\\ $\bf{(3)\;\;\int \frac{\sqrt{x^4+1}}{x^4-1}dx}$\ ...
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lim sin[x]/[x] as x→0 ...
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SOLVE dy/dx=1/(x^2+y^2) ...
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*Image* ...
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If the area enclosed between x2+y2≤9(pi)2 and sin(x-y)≥0 is m(pi)3/n sq units,then find [m]-[n]+[ m+n/m-n ]? ...
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1)If \dpi{100} \fn_jvn \int_{a}^{b}(2+x-x^{2}) is maximum find a+b? 2)For f(x)= 6/1+31ex the possible number of different integral values which f(x) can take is? 3)if \dpi{100} \fn_jvn \lim_{x\rightarrow \infty }\sqrt[3]{8x^{ ...
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If y=x dy/dx + dx/dy then find y when x=4? ...
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if f(x)= 1/3 (f(x+1)+ 5/f(x+2) ) and f(x)>0 and finite for all x belonging to R,then limx→∞ f(x) is a) 2/5 b) 5/2 c) 10 d)0 ...
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\hspace{-16}\bf{(1)\;\; \int_{e^{e^{e}}}^{\infty}\frac{1}{x.(\log x).({\log \log x}).(\log \log \log x)^{\frac{4}{3}}}dx}$\\\\\\ $\bf{(2)}$ For Which Integer $\bf{ 1\leq m\leq 10}$ is it true that\\\\\\ $\bf{\int_{0}^{\pi}(\c ...
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Let the range of the function f: R→ R f(x) = | x-1| + |x - a| + | x| + |x+1| + |x+ 2a - 21 | a being a real parameter given by [α,∞).Then find the no. of integral values of a for which there is exactly one x0ε R such th ...
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i,j positive integers f(i,i+1)=1/3(for all i) f(i,j)=f(i,k)+f(k,j)-2f(i,k)(k,j) Find the value of f(1,100) ...
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show that ∫[sspi][/ss0]|(sin nx)/x|dx ≥ (2/pi)|1+(1/2)+(1/3)+.......(1/n)| ...
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let f(x)=∫(0 to 1)|t-x|tdt for all real x. What is the minimum value of f(x). ...
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limx→0+ (sin x)sin x = ? ...
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∫ Sinx/x =?? ...
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\hspace{-16}\bf{\int_{0}^{\frac{\pi}{2}}\frac{\sin(2nx).\sin x}{\cos x}dx\;\;, }$ Where $\bf{n\in \mathbb{N}}$ ...
repliedJun 25 '13 at 22:13
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