Recently Active Calculus Questions

i have a dbt in evaluating this limit,the buk has a diff ans *Image* ...

the statemnet is sin4π{x}=sin(4πx) for all x εR its given to be true... but i dont think it to be.... what do u say ? ...

∫dx/cosx√cos2x ...

D interval in which y=x2e-x is increasing is A. (-∞,∞) B.(-2,0) C.(2,∞) D.(0,2) & also show how u did this. ...

Let f(x) = max{x,0} for all x belonging to R and f(xy) is not equals to f(x) f(y), then show that x <0 , y<0 ...

does the limit exist- limx-0xsin1/x ...

plz solve this one.... ∫ dx/sin5x + cos5x ...

if f(x) has domain [0-1] and range [0-1] and iscontinuos n differneitable show dat for sum x...f(x)=x ...

f(x) = e2x. Then the normal to the curve f(x) passes through (a) (0,1) (b) (lne, e2) (c) (1/2, e) (d) (-1/4, 1/√e) ...

f(x)=(cosx)(sinx + sin2x + sin2t ) find range of f(x) if t is a constant.(answer in terms of t) ...

\lim_{0}(tanx/x)^{1/x^{2}} (x is tending to 0) ...

let f(x) be such that f(xy)=f(x)f(y)....if f(x) is continuos at x=1,show dat f(x) iscontinuous at all x ≠0 ...

Q Solve \lim_{x\rightarrow 0}\frac{sin\frac{1}{x}}{\frac{1}{x}} ...

Ans is coming but method is very long.. is there any shorter method ?? x3 + y3 = 3axy P.t d2y/dx2 = 2a2xy/(ax-y2)3 ...

Ques1) Let f p (@ ) = (cos@/p2 + i sin @ / p2). (cos 2@ / p2 + i sin 2@ / p 2 )...................................(cos@ /p + i sin @/p). Then lim n→∞ [|fn(2 ∩ )|] is equlas to , where [.] denotes greatest integral funct ...

integrate dx/((x^2) (1+(x^4))^3). ...

Let P(x) be a polynoimial of degree n with real coefficients and is non negative for all real x,tehn prove that P(x)+P'(x)+...+Pnx is non negative for all x ...

Given 1∫2 ex2 dx = a , Find the value of e∫e4 √(logex) dx . ...

Ques1) Solve ∫ √ (x-3 ) { Sin -1(ln x) + cos -1 (ln x) } dx (a) (x-3) 3/2 + c (b) 0 (c) does not exists (d)none of these Ques2) Show that , if n is an odd positive integer, then ∫ |x n | dx equals to (|x n| x ) / (n+1) ...

If a, b, c belongs to R satisfy 7a/3 + 3b/2 + c = 0, then atleast one root of the equation ax2+bx+c = 0 lies between a. (3, 4) b. (0,2) c. (3/2, 2) d. (1, 3/2) ...

f(x) is a continuous function, which is twice differentiable - function is from Reals to Reals. Given |f(x)|\le 1 for all real x & |f''(x)|\le 1 , again for all real x. Prove |f'(x)| <2 for all real x. ...

Prove that for a cubic function tangent lines at two distinct points will never coincide ...

13) Period of the function f(x) = sin{sin(∩x)} + e(3x) , where {.} denotes fractional part, is a)1 b)2 c)3 d)6 14)The min values of the function f(x) = {sin-1(sinx)}2 - sin-1(sinx) is a)∩/4(Π+ 2) b)Π/4(Π-2) c)Π/2(Π+2 ...

f(1/x)+x2f(x)=0 for all x>0 and I=\int_{1/x}^{x}{f(z)dz} 1/2<=x<2 i did like this f(1/x)+x2f(x)=0 ----------(1) replace x by 1/x =>f(x)+1/x2 f(1/x)=0 Now dI/dx=f(x).1 -(-1/x2 f(1/x))=> dI/dx=f(x)+1/x2 f(1/x) dI ...

Ques) If f1(x) = (x/2) + 10 , for all x belonging to R and defined by f n (x) = f1 { fn-1 (x)}, for all n≥2. Then show that lim n →∞ fn(x) = 20 I try to solve it this way, f1(x) = x/2 + 10 = (x+20) /2 Similarily, f2(x)= ...

These are few good probs that i've been unable to solve pls solve these for me. 1)If the line ax+by+c=0 is normal to the curve xy+5=0, then a and b have (a)same sign (b)opposite sign (c)cannot be discussed (d)none of these 2) ...

1) If f(x) = lim n→ ∞ n ( (x) 1/n -1 ) for x>0, y>0 , then show that f(xy) = f(x) + f(y) 2) Solve lim x→0 [1+log cos 2 x/2 cosx] 2 ...

d range of d function 4{x}3-3{x} ...

A simialr ques on area was posted a few days back..here is another one f(x)=\sin x g(x)=\begin{Bmatrix} (max f(t),0\leq t\leq x) &0\leq x\leq \pi \\ (1-\cos x )/2& x> \pi \end{Bmatrix} Discuss continuity and differentiabli ...

I was amazed by this solution... Never saw this trick.. I hope this helps some of you... I =\int\frac{x^{2}}{(x\sin{x}+\cos{x})^{2}}dx Before giving the complete solution... Let me give this hint so that some of you can apply ...