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1. If f(x) = \lim_{x\rightarrow \infty } \frac{1}{1+nsin^{2}\pi x} , find f(x) for all real values of x. 2. 2f(x) + f(-x) = 1+x, find f'(10). 3. If a,b,c are in GP such that a+b+c = bx. Find all x satisfying the above relatio ...
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1 > Prove that if " an " is a sequence of real numbers such that , " lim ( n → ∞ ) [ an ] = x " then , " lim ( n → ∞ ) [ a1 + a2 + ...........an/n ] = x " also . Source - Michael Spivak ...
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Let f(x) , x greater than equal to 0 , be a non negative continuous funcn , and let F(x) = 0∫x f(t) dt , x greater than equal to 0. If for some c >0 , f(x) is less than equal to c F(x) for all x greater than equal to 0, ...
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1. \lim_{\theta \rightarrow \frac{\pi}{4}} \frac{\sqrt{2}-cos\theta -sin\theta}{(4\theta-\pi)^{2}} 2. \lim_{x\rightarrow 0}\frac{xtan2x-2xtanx}{(1-cos2x)^{2}} 3. \lim_{x\rightarrow 0}\frac{e^{x}-e^{xcosx}}{(x+sinx)} I want to ...
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is this true/false 'degree of diff eqn represents no. of family of curves' i think its false pl confirm this ...
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Diffrenciate |x| w.r.t x using first principle. ...
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f is a real-valued differentiable function defined on [0,1]. If f(0)=0 and f(1)=1, then prove that there exist distinct points x1,x2 in [0,1] satisfying 1/f'(x1) + 1/f'(x2) = 2 ...
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Is "calculus and analytic geometry by thomas and finney" good for concept clearence? Or any better choices ? ...
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if number of function defined from f={1,2,3,4,5,6}→{7,8,9,10} such tht the sum of f(1)+f(2)+f(3)+f(4)+f(5)+f(6)=odd number is 2n .then find the value of n??? ...
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$If $m\in\left(0,\frac{5}{6}\right)$. Then Calculate value of $m$ in \\\\$\int\limits_{0}^{2}\left|\frac{1}{3}x^3+mx^2-2x-2m-\frac{1}{3}\right|dx=4$ ...
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$Calculate $\int_{0}^{\frac{\pi}{2}}cos^{2009}x.cos(2010x)dx=$ ...
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∫pi0 1/1+tanx dx ...
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*Image* ...
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∫0pi/4 2tanxsinx/1+sin2x dx ...
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A function F:R→R+ is such 2F(x+2)+F(x+1)y+F(x+4)=0,24F(x+2)-2y+3=0 and F(0)=2.If ∫f(x)dx=F(x) +C and∫01f(x)dx=2 then find the value of ∫01f(3x)dx. ...
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let F(x) and G(x) be two cubic polynomial functions such that F(G(x))=G(F(x)). F(0)= -24, G(0)=30 find the value of F(3) + G(6) ?? ...
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Find ∫ ex/x dx. ...
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y = (-1)^{[x]} , where [.] is GIF. Don't take help of softwares n all that ...
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*Image* IF a thread is let loosely hanged under the infuence of →g where distance between the ends to which it is hoked is d and length of string is L then find the height????????????????????????? ( actually i want you to f ...
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Given a function, f differentiable on (0,∞) & the limit as x→∞ of (f(x)+f'(x))=0. Find the limit of f(x) as x→∞. ...
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Can ex be differentiated at the point 0. ...
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*Image* find f(x) ...
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*Image* ...
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find f(x) if f(x+y)=f(x)+f(y) such that f(x) is continuous at 0. ...
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i request u guys if u can provide a few problems and their solution based on taylor and maclaurian series within constraints of jee,of course thanx a ton! ...
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if f(x+y)=f(x)g(y)+g(x)f(y) and g(x+y)=g(x)g(y)-f(x)f(y) prove that f(0)=0 and g(0)=1 ...
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If F''(x) + F(x) = 0 F'(0) = 0 F(0) = 0 prove that F(x) = 0 for all real x ...
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find the area of the ellipse given by the equation x2/a2 + y2/b2 = 1 ...
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lim(x→0) (sin xn)/x = pi/180 for n=? ...
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Range of the function f(x)=ln[cosxcosx+1],xE(0,pi/2) (A)(ln(1+e 1/e ),ln2) (B)(ln(1+ 1/e 1/e )ln2) (C)(0,ln2) (D)None of these Ans.(B) is the correct choice. ...