Recently Active Calculus Questions

∫ dx/sec x+cosec x and ∫ 1/3√x+4√x + log(1+x1/6)/ x + x dx ...

1) \int_{0}^{2a}\sqrt{2ax-x^{2}} 2) \int_{-1/2}^{1/2}\left ( [x]+ln(\frac{1+x}{1-x}) \right )dx 3) \int_{-2}^{2}\frac{3x^{5}+4x^{3}+2x^{2}+x+20}{x^{2}+4} ...

1) find the sum of the series \frac{1}{4!}+\frac{4!}{8!}+\frac{8!}{12!}................\infty 2) if a function defined such that f:R→R f(x)-2f(\frac{x}{2})+f(\frac{x}{4})=x^{2} find f(x) 1st one is a doubt[1] ...

If *Image* and f is differentiable function satisfies : *Image* *Image* then find f(x) not a doubt....jus found it gud ...

*Image* i m not able to prove > but i m getting x>=sinx!!!! is the question correct?????? ...

f is a continuous function that maps the closed unit interval I = [0,1] into itself. Prove that if f(f(x)) = x for all x ε I, then f is monotonic ...

*Image* why have they used h---->1 for LHL and h----->0 for RHL??can u account for this! ...

1)Find the value of "t" for which- e2x= t x , has only one solution. 2)Let "g" be the inverse function of a differenciable function "f" such that, G(x) = 1/g(x). If f(4)=2 & f'(4)= 1/16, then (G'(2))2 =? 3) Value of "a" for w ...

Functions f(x) & g(x) are such that - (f.g)'= (f'.g'). If f(x) = ex2 and g(1)=e, the domain of g(x) being (1/2,∞), find (a+b) if g(5) = aeb. ...

f(x)=ax3+bx2+cx+d g(y)=ay3+f'''(m)y2/2+cf''(m)/1+f(m)=0. f(x) has roots α1, α2, α3 and g(y) has corresponding β roots. PT difference between the corresponding roots are equal. ...

*Image* ...

*Image* ...

Q1 let f:R→R be defined as f(x)= x2+ax+1/x2+x+1 .the set of all exhasutive values of a for which f(X) is onto ans given is φ..it is wrong naa ?? Q2 whats min value of (sin-1(sin(x)))2-sin-1(sin(x)) Q3 if f(x)=x(2-x), 0≤x ...

*Image* ...

*Image* ...

*Image* ...

it was a simple sum but its aftermath wa too much d/dx of under root 1-cos2x/1=cos2x (means whole function under root) easily solved it to tan^x now under root means tan x so answer sec^2 x simple but not the right answer ans ...

Discuss continuity of e[log{l{x2}l2}] and draw its graph where all brackets have their usual meaning... dont hesitate to tell me if it is not solvable at our level ...

f(x)=x2-4x g(x)=min f(t) ; x≤t≤x+1 ; 0≤x<4 i know this type ahs been discussed before...but i just need graph to check myself....no calculations....[1] ...

limn→∞sin2(π (n!)2-n! ) ...

Q1 \int_{a}^{b}\frac{e^{x/a}-e^{b/x}}{x}dx Q2 \int_{0}^{1}\frac{lnx.ln(1-x)}{(1+x)^2}dx ...

The value of the definite integral I = ∫ [ 0 to Π][ x (1+l cos x l ) ] dx = ? (A) 2 2 Π(B) 2 Π(C) 2 Π(D) 4 Π...

∫e^x(1+sinx)/(1+cosx) ...

MULTIPLE ANS QS 1) Lt x--->2 [(f(x) -9) / (x-2)] = 3 Then Ltx-->2f(x) is ? (A) 2 (b)5 (C) 9 (D)12 ...

1) f(x) = i) Sin[x] ; [x] ≠0 [x] ii) 0 when ; [x] = 0 Find -- Lim (x→0) f(x). 2) Lim(x→∞) {(x+6)/(x+4)}x+4 = ? 3) If x>0, Lim(x→0) {(sinx)1/x +(1/x)sinx} = ? 4) Lim(x→ -∞) {x4 Sin(1/x) +x2}/{1+ lx3l } = ? ...

Q1. \lim_{x\rightarrow 0}\frac{sintanx+ln(\sqrt{1+sin^2x}-sinx)}{ln(1+x^3)} Q2. A=\begin{bmatrix} 1 &1 &1 \\ -1 &0 &2 \\ 2 &1 &0 \end{bmatrix} , I is the unit matrix of order 3X3 and aA3 + bA2 + cA + I = B where B is null mat ...

1. lim na sin2n!/n+1 n→∞ a E (0,1) is equal to (a) 0 (b) 1 (c) ∞ (d) does not exist 2.lim {11/sin2x + 21/sin2x+....+n1/sin2x}sin2x x→0 3. lim xn+nxn-1+1/e[x] x→∞ ...

DOUBT f(x)= ax2+bx .FInd all possible values of 'a' such that there exist at least one positive value of 'b' for which both domain and range of f(x) lie in same set ...

\int_{0}^{[x]}{(\int_{0}^{[x]}{([x]-[x-\frac{1}{2}])dx)dx}} ...

not a doubt I\! f \;\; 2f(x) + f(-x) = \frac{1}{x}sin(\frac{x^2-1}{x}) , F\! i\! n\! d \; \; \int_{1/e}^{e}{f(x)dx} ...