Recently Active Calculus Questions

Can anyone plz explain the use of complex numbers ( de-moivre's theorem) in finding out the integral of type ∫sinmxcosnxdx , where both m,n are positive integers. ...

let f:R-->R is a continous function on [1,3].let f(x) takes rational valeus for all x.if f(2)=10.f'(2)=0.find f(x) and f(1.5) ...

1st one is JEE 2010 quesn..... Lest s ={ 1 , 2 , 3 , 4 } . What r the total no. of unordered pairs of disjoint subsets of S ? 2. Let {x } and [x ] denote the fractional and integral part of a real no. x respectively. solve 4 ...

1) \int \frac{x^3+x+1}{x^2-1}dx 2) \int \frac{tan\theta +tan^3\theta }{1+tan^3\theta }d\theta 3) \int \sqrt{cotx}dx ...

1. If f: [-1 , 1] -> R and f ' (0) = limit n tends to infinity nf (1/n) and f(0) = 0 . Find the value of lim n tends to infinity 2/pi (n+1) cos inverse (1/n) - n . Given that 0< mod ( limit n tends to infinity cos inver ...

*Image* rrom arihanr ...

FIND THE DOMAIN OF (X-1)/X-2{X} ?WHERE {.} DENOTES.FRACTIONAL X?? ACORDING TO THE GIVEN ANSWER IS- (-∞,0)U(0,1]U[2,∞).. BUT I DONT THINK THE ANWER IS CORECT BCOZ U TAKE ANY POINT IN [1,2] THE POINT WILL SATISFY THE GIVEN ...

in the fuct. f(x) = | Sin x | ...... which points are described as non-diff points...... i 've ans it as at x=nπ , n ε I.... the grapgh will be non-differential,..... but the ans given in the buk is at only x=0 , the graph ...

1) If t be a real number satisfying the equation 2t3 - 9t2 + 30 - a, then find the values of the parameter 'a' for which the equation x + 1/x = t gives six real and distinct values of x. ...

*Image* this is 0 to pie *Image* this is indefinite ...

prove that for all real x,y the value of x2 + 2xy + 3y2 - 6x - 2y cannot be less than -11. ...

Q) y ≥ √(1-x2), max( !x!, !y!) ≤ 4 The slope of a family of lines is defined as m(t) = -sin2t + sint + 1, where (t, 2t+0.4) lies inside the region R. 1) The maxmvalue of the slope of any member of family is for t = (a) ...

P(x) be a polynomial of at most degree 5 which leaves remainders -1 and 1 upon division by (x-1)3 and (x+1)3 respectively. 1) Number of real roots of P(x) = 0 (a) 1 (b) 3 (c) 5 (d) 2 2) The maximum value of y=P''(x) can be ob ...

1. *Image* differentiate it 2.if f '(x) = sinx + sin4x.cosx , then f ' (2x2+∩/2 ) is ...

I could not solve this for quite sometime... lets see who can ... let f(x)=(2x-Ï€)3 + 2x - cos x find d/dx [f-1(x)] at x=Ï€ [1][1][1] ...

plz can ne1.... provide me the graph 4 f(x) = sin n x n= 1,2,3,.......... ...

let y=f(x) be differentiable function for all x belongs to R . then which one of the following is always true : (a) d2y/dx2 - (dx/dy)3 =0 (b) d2y/dx2+ (dy/dx).d2x/dy2 =0 (c) d2y/dx2 - (dy/dx)3 = 0 (d) none of these ...

hey friends wht will be the differention for {x} and [x]?????? further,,, hw will u diff y = {x}/[x] {.} represents fractional part of x [.] represents greatest integer of x ...

Lim (n → ∞) <summation> r=1 to n tan-1 ( 1/r2+3/4 ) plz help me out in this..... facing a bit prob... ...

(1) The no. of solutions of the equation 2^{\left|x \right|}\left(\sqrt{1-x^{2}} \right)=1 is ? (2)The order of the differential equation y=C_{1}e^{x+c_{2}}+C_{3}e^{x+c_{4}} + C_{5}\sin (x+C_{6})+C_{7}\cos (x+C_{8}) is equal ...

1) Consider two functions f(x)=1+ e^{\cot ^{2}x} and g(x)= \sqrt{2\left|\sin x \right|-1}+ (\frac{1+\cos 2x}{1+ \sin ^{4}x}) Statement-1: The solutions of the equation f (x) = g (x) is given by x=(2n+1)\frac{\Pi }{2} for all ...

1.) limn→∞ [1/n+ n2/(n+1)3+ n2/n+23.... 1/8n ] 2.) lim 1/n[sec2π/4n+ sec22π/4n...sec2nπ/4n] n→∞ 3.) limn→∞ *Image* ...

can ne1 explain me how is it that Lim (x→0) [ sin x/x ] = 0 nd similar case for tan x [.] is GIF.... wht is the value of [cos 0] .... is it 0 or 1.... i m confused// ...

If P(x) be a polynomial such that P(x2+1) = {P(x)}2+1 and P(0) = 0 then P'(0) is equal to : (a) 1 (b) -1 (c) 0 (d) none ...

find the period of following function: f(x+\lambda ) = 1 + \sqrt{2f(x) - f^{2}(x)} i have a doubt in answer ...

what will be Lim (x→∞) (x+2)tan-1(x+2) + xtan-1x i m 'ving doubt in this..... plz help ...

check given function f(x)=Ix+2I verifies lagrange's theorem on :- a) [-2,4] b) [-3,4] c) none of these here I DENOTES MODULUS.... ...

find limit n tends to infinity ( 1/1.4 + 1/4.7+..........+1/ (3n-2) ( 3n+1) ...

can ne1 plz explain me in brief how can we draw the graph of h(x) = f(x) + g(x) i.e., the sum of two functions...... e.g., y = x+sin x y = x2+x3 y= x + 1/x is dere any direct approach for such graphs or we need to find maxima ...

Hey friends.... facing a bit prob in finding summation... plz help lim(n→∞) <summation>r=1 to n ( r/4r2+1 ) i think the answer shud be ∞ as the degree of Nr is less than the degree of Dr..... plz let me know my mi ...