Recently Active Calculus Questions

q1 Find intervals of continuity,differentiability 1) sin-1( 1+x2/2x ) 2) [x[1-x]] [.] denotes Greatest Integer function q2 Find Domain and range 1/[sinx] q3 f(x) and g(x) are twice differentaible functions in [0,2]. If f"(x)= ...

Q12 added [1][1] 1) \int \sqrt{\frac{(1-cos\theta )}{cos\theta (1+cos\theta )(2+cos\theta )}}d\theta ans..................> cosec^{-1}(2cos^{2}\frac{\theta }{2})+c [ when solved will add new questions here.] 2) 2) \int \fr ...

if y(1)=1 , y'(1)=1 and xyy''+xy'2 =3yy' then find y2(2) ??? 8.5 ...

f(x) = 1/(x-2) is x=2 a critical point ? ...

Multiple option type Let f: \left[-1,1 \right] onto \left[3,5 \right] be a linear polynomial.Then which of the following is true? (A)f(-\frac{1}{2})=\frac{7}{2} \: (B)f(-\frac{15}{4})=\frac{1}{4}\: (C)f(0)\neq 4 \: (D)f(\frac ...

plzzz integrate this ∫ 1/1+5cosx from 0 to Π...

1)if *Image* then the range of f(x) is? 2)if the function f(x)=sinx+cosax is periodic, then a must be a)a rational number b)an integer c)any real number d)irrational ...

\int \frac{x^4-1}{x^2(x^4+x^2+1)^{\frac{1}{2}}}dx ...

Let f (x) is a continuous function which takes positive values for x≥0 and satisfy \int_{0}^{x}{f(t)dt}=x\sqrt{f(x)} with f (1) =1/2. Then the value of f(\sqrt{2}+1) equals 2 ??? ...

solve the following \int_{0}^{\pi }{\frac{\sin ^2n\theta }{\sin ^2\theta }}d\theta ...

plz post the solutions for these questions 1) find the value of \int_{0}^{100}{[tan^{-1}x]} where [] equals gretest integer function 2)find the value of \int_{-2}^{2}{min {x-[x],-x-[-x]}dx } where [] denotes greatest integer ...

1)\lim_{x\rightarrow 0}\frac{sin(\pi cos^2 \pi)}{x^2} Π(pi) 2)lim x→1 (1+cos \pi x)cot^2 \pi x 1/2 3)\lim_{h\rightarrow 0}[\frac{1}{h^3\sqrt{8+h}}-\frac{1}{2h}] -1/48 4)\lim_{h\rightarrow 0}\left[\frac{(a+h)^2sin(a+h)-a^2s ...

How many possible ways to : ∫ dx/x ...

find the domain of f(x) f(x)=cos-1 1+x2/2x + sin(cosx) please help!! ...

1) Find the value of y(log4), if y2 -7y1 +12y=0, given that- y(0)=2 & y1(0)=7. 2) :: Done :: If a function f(x) satisfies- i) f(x+y)= f(x).f(y) ii) f(x)= 1 + x.g(x), where Lim(x→0) g(x)=1. Find the value of logf(8). (Ans - ...

Wikipedia (http://en.wikipedia.org/wiki/Integration_by_parts) mentions LIATE rule to be followed when integrating by parts,whereas I have studied ILATE rule. Which is appropriate method ? ...

What is d cosine of angle of intersection of the curves: y=3x-1 logx and y=xx-1... ...

If "f" is a Decreasing Odd fn., f-1 is - a)Odd, Decreasing b) Odd, Increasing c) Even, Decreasing d) Even, Increasing ...

Q1. Let \begin{Bmatrix} x_{n} \end{Bmatrix} be a sequence of real nos satisfying the recurrence relation x_{n+1}=\frac{x_{n}\sqrt{3}-1}{\sqrt{3}+x_{n}}, \; n\epsilon N Then the period of the sequence is got the answer .. but ...

The value of \int_{a}^{b}{(x-a)^3 (b-x)^4 dx } is a) (b-a)4/64 b) (b-a)8/280 c) (b-a)7/73 d) None Of These (ans given in book is b) ...

hello every one in targetiit taking some hint from PrItIsH Da i thot of startin an thread for integration ( similar kind of prctc was folowed at mathlinks too) will post integrals myself and d person who answers the integral ...

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This qsn came in FIITJEE AITS 2day. I_n=\int_{\frac{\pi}{2}}^{\propto}{e^{-x}cos^{n}xdx}=\frac{720}{3145}e^{-\frac{\pi}{2}} This holds for n=2m, where m is a natural number. Find it. ...

y2 = 2c(x+ c ) find order and degree iit qsn After double differentiation im getting yy''+y'2=0 from this order is 2 and degree is 1 but it's wrong Ican not understand why it's wrong Hel[p me in solving this Q. ...

statement 1: 0∫Π1/1+5cosx=Π/2 statement 2:0∫af(x)dx=0∫af(a-x)dx ...

** edited ******* ...

1) find maxima of xy2z3 provided : x + y + z = 6. 2) find maxima of (x-3)2 + (y-2)2 provided : (x+3)2 + (y+2)2 = 4 ...

∫(x7m+ x2m + xm).(2x6m + 7xm + 14)1/m.dx (Have seen these sort of Qn(s) b4 too,,,A hint to start wud be enuf...) ...

1) cos (x+y) dy = dx 2) x+y dy/dx /y-x dy/dx = (1 + x2/y2 ) ( ln ( x2+y2 )) 3) dy/dx = (4x + y + 1)2 4) 2x3y3 + x4y2 dy/dx = -b2/a2 y - b2/a2 x dy/dx [ GUYS POST THE SOLN. FULL AS I CANNOT CONFIRM UR ANS. SINCE I DON'T HAVE T ...

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