Recently Active Calculus Questions

∫ dx / (x + √x2-1)2 = ? ( here its a whole square root) ...

The nth therm of a sequence in given by nn/n! .... Show that this sequence converges and find it's limit... ...

1) Find the values of a for which the eqn 3x4 + 4x3 -12x2 + a = 0 are real and distinct. 2) If f ' (sinx) < 0 and f '' (sinx) > 0 for x belonging to R, then find the intervals of monotonicity of the function g(x) = f(si ...

1) Let f(x) = x3+x2+100x+7sinx then show that the eqn 1 / [y-f(!)] + 2 / [y-f(2)] + 3 / [y-f(3)] = 0 has exactly one root lying in (f(1) , f(2)). 2) Let f(x) and g(x) be two functions which cuts each other orthogonally. At th ...

Find the domain of the following:- (a) F(x) = sin -1{ (2-3[x] ) / 4 } (b) F(x) = sin |x| + sin -1 (tanx) + sin (sin -1 x) (c) F(x) = (x 2 - |x| - 2) 1/2 ...

Lim (x→∞) 2t-3t/xn where t= xn/ex and n ε N = a.ln(2/3) b.0 c.n ln(2/3) d. not defined ...

Q. how would we prove that that the following statement is wrong n+n+n......n times = n2 differentiatng both sides w.r.t n we get 1+1+1+.....n times = 2n or n=2n or 1=2 ...

Prove that ∫ dx/1+xn ( LL= 0 and UL= ∞) = ∫ dx/(1-xn)1/n (LL=0 AND UL=1)(n>1) LL=LOWER LIMIT UL=UPPER LIMIT ...

∫ {1/(x16 - 1) }dx ...

Ok here r a few ques i found quite tricky...well at least to me they were tricky..and hence i cud not solve them:)so pls do me a favour and solve them for me. 1)Solve |2x-1/x-1|>2 2)Solve |x/x-1|+|x|=x2/|x-1| 3)solve (x+3) ...

lim n->∞ (an + bn)1/n also 0<a<b ...

Ques1) Let g(x) = {log(1+x)} -1 - x-1 , where x>0, then (a) 1<g(X)<2 (b) -1<g(x) <0 (c) 0<g(X)<1 (d) none of these Ques2) Show that the interval in which x3 increses more rapidly than 6x2+15x+5 is (5,infi ...

If f: R →[Π/6, Π/2), f(x) = sin-1 (x2-a)/(x2+a) is a onto funtion, then set of values of 'a' is: a. {-1/2} b. [-1/2. -1) c. [1/2. -1) d. {1/2} ...

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consider a square with vertices with at (1,1),(-1,1),(-1,-1),(1,-1).let S be the region consisting of all points inside the square which are nearer to the origin than to any edge .sketch the region S and find its area ...

can somebody suggest a good book on calculus..specially integration i have A das gupta ......it doesn't illustrate some good examples for learning how to integrate ...

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∫ 555x * 55x * 5x dx = ? ...

consider a triangle OAB formed by O≡(0,0), A≡(2,0)AND B≡(1, 3 ). P(x,y) is an arbitrary interior point of the triangle moving in such a way that the sum of its distances from the three sides of the triangle is 3 units . ...

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f(x)=1 + 2 sin x + 2 cos2x, 0≤x≤pi/2 A. f(x) is greatest at pi/6 B. f(x) is least at 0,pi/2 C. increasing in (0,pi/6) and decreasing in(pi/6,pi/2) D. f(x) is continuous in [0,pi/2] ...

To add to the action already taking place in this forum: Prove that e^x\geq 1+x\quad\forall \,x\in\mathbb{R} , the set of real numbers (easy part.) Using this result, prove the Arithmetic Mean - Geometric Mean inequality for ...

what is a non integrable function??? i know non differentiable function but can't really make out what the former means!! ...

A Few reasoning and assertion questions -: f(x) = lim cos(n!2∩x) n is an integer . n--->∞ g(x) = lim cosn(2∩x) n--->∞ h(x) = lim {cos(n.x)+2}-n Range of f = R1 , Domain Of f is D1 Range of g = R2 , Domain Of g i ...

Integrate ex2 ...

If f(x)=sin x + a2x + b is an increasing fn. for all values of x,then -- A. a ε (-∞,-1) U (1,∞) B. a ε (0,∞) C. a ε (-1,1) D. none of these ...

Try proving Lagrange's mean value theorem. ...

sqrt[tan x]dx ...

\int_{-2}^{2}{\frac{sin^2x}{[\frac{x}{\pi }]+0.5}}dx where [.] =GINT ...