Recently Active Calculus Questions

1)Is there any short cut method to solve this prob: If f(x)=x+1/x, find f[f{f(x)}] 2)Can anyone show me the graph of cos√x? ...

Pls solve the following for me.Or if they are too big then at least give some proper "user-friendly" hints.(solve the 3rd one first--its i think is easy n urgently reqd) 1)Find the sum of the intercepts on the axes of coordin ...

x cosx dy/dx + y(x sinx + cos x)=1 ...

A channel 27m wide falls at a right angle to another channel 64m wide.the greatest length of a log that can be floated along the system of channel is,...... a.100m b.110m c.120m d.125m ...

Ques1) If f (3x-4 / 3x+4 ) = x+2 then show that ∫ f(x) dx is -8/3 log 3 |1-x| + 2/3 x +c Ques2) If ∫ x log (1 +1/x) dx = f(x) ln (x+1) + g(x) ln x^2 +Lx +c, then choose the correct alternative/s (a)f(x) = x^2 /2 (b)g(x) = ...

How many real roots does function f(x)=xn+px+q can have for n even and n odd(>3) ...

Let f(x+y)=f(x).f(y) for all real values of x & y.f(5)=2, \frac{\partial (0)}{\partial x} =3. then \frac{\partial (5)}{\partial x} =? a.6 b.3 c.5 d.1 ...

*Image* ...

At what values of m does the integral ∫20 1-cosx dx/xm converge? ...

*Image* ...

An+1=(An+(a/An))/2 , where A1>0,a>0. Find Limn→∞An ...

if f(x) belogs [1,2] when x belongs R and for a fixd positive real no P. f(x+p)=1+ 2f(x) -f(x)^2. prove that f(x) is periodic. ...

*Image* 1.1.4 and 5 ...

1) The value of lim x→ ∞ (x+2) tan -1 (x+2) - (x tan -1 x) is (a) pie/2 (b) does not exists (c) pie/4 (d) none of these 2) Show that the value of lim n → ∞ (1 / n3) ( [ 12x + 12] + [ 22x+22] + .....................+ [ ...

Ques1) Solve the integral *Image* ...

Determine all functions (from R → R) \boxed{xf(x+xy)=xf(x)+f(x^2)f(y)} FOR ALL REALS X,Y..... ...

*Image* anyone finding the area....pls upload a graph too... ...

∫[tan-1x] from -10 to 10 []→ denotes gratest intiger funtion ...

At what point does the function f(x)=(ax+b)/(cx+d) has no maxima or minima ...

In a triangle ABC , find the least value of, cot A/2 * cot B/2 * cot C/2 * cos A/2 * cos B/2 * cos C/2 ...

lim (11+a1/x+(a+1)1/x+...+(a+n-2)1/x)x x→0 a>2 and nεN ...

Let f(x) = 2007^{x}/(2007^{x}+\sqrt{2007}) then the sum f(1/2007) +f(2/2007)+.............................f(2006/2007)=? a.1004 b.1003 c.1003.5 d.1004.5 ...

1) If k sin2x + (1/k) cosec 2 x = 2, for all x belonging to (0, pie/2) then cos2x + 5 sinx cosx + 6 sin 2x is equals to (a) (k2+5k+6) / k2 (b) (k2-5k+6) / k2 (c)6 (d) none of these choose the correct alternative 2) If lim x↠...

(y+ y3/3 + x2/2 ) dx + ( x+xy2/4 )dy = 0 solve the above differential equation ...

Let f:R→R such that for all x,y belongs R *Image* where n belongs N.Prove that f(x) is a constant function. ...

Plz sketch the graph of (x2-x+1)/(x2-3x+2) ...

Evaluate the integral: \int_0^1\dfrac{x-1}{\ln x}\ \mathrm dx ...

Find \lim_{n\rightarrow \infty}{\frac{a^n}{n!}} I have this soln available with me.. *Image* plz provide a new shorter soln..or help me to understand this soln.. ...

1)f(xy)=f(x)+f(y) implies f(x)=klnx or f(x)=0 2)f(xy)=f(x).f(y) implies f(x)=x^n 3)f(x+y)=f(x).f(y) implies f(x)=a^kx 4)f(x+y)=f(x)=(fy) implies f(x)=k where k is a constant and 5)f(x).f(1/x)=f(x)+f(1/x) implies f(x)=±x^n +1 ...

find coordinates of point on parabola y2=8x which is at min distance from circle x2+(y+6)2=1 is differentiation the only method ?? can we get answer by observation only ?? ...