Recently Active Calculus Questions

\int_{0}^{2a}{x^3(\sqrt{2ax-x^3)}}dx ...

1) Find the no. of solutions of logx3 = 5x-7. 2) If a line intersects the curve - y= x4 +cx3 +12x2 -5x +2 in 4 distinct points, find the possible integral values of c. 3) Let a function f be defined as - f : {1,2,3,4} → {1, ...

someone solve this one... ∫ xxdx ...

suppose i have a function y = 3/ 2 x logx +3/4 i know the graph of logx but how will i draw the graph of the above function??? wat happens wen a constant is multiplied with the variable wat change takes place in the graph and ...

If A+B+C=Pi , then prove that cos A+cos B+ cos C<3/2, where A, B, C are distinct. solve using graph ...

(1) \int_{0}^{\pi }{|\sqrt{2}sinx+2cosx|dx}= (2) If \int_{0}^{1}(ax+b)/(x^{2}+3x+2)^{2}dx = 5/2 then find value of a and b ...

solve differential equation. \frac{dy}{dx}=\frac{x+y+1}{x-y} ...

find the of set values of a for which f(x)=( a+4 /1-a -1)x5-3x+loge5 decreases for all x ...

f(x) = 1 +x , 0 ≤x≤2 = 3 -x , 2 < x ≤ 3 then f(f(x)) at x= 1 is [a] 1 (b] 3 i kno d method , so pls only tell wich one is d ans acc to u ? ...

If y = sinx/1 + cosx/1 + sinx/1 + cosx/1 + ............ upto infinty. then prove ; \frac{dy}{dx} = \frac{(1+y)cosx+sinx}{1+2y+cosx-sinx} ...

sry question got posted twice ...vry sorry for dat , nishant sir remove dis post , btw da question is here http://targetiit.com/iit-jee-forum/posts/functionssss-13844.html [1] ...

Q) The tangents that are parallel to the bisector of the first co-ordinate angle for the curve F(x)= ∫0x 2tdt are a) y=x- 1/4 b) y=x+ 1/4 c) y=x- 3/2 d) y=x+ 3/2 ...

Q1 \ \int \frac{dx}{x^{22}(x^7-6)} Q2 \ Let \ t(x)=u(x)-v(x) \ where \ u(x)=sin^62\pi x \ and \ v(x)=lnx Prove \ area \ enclosed \ by \ u(x) \ and \ v(x) \ is \sum_{r=0}^{n}{\int_{x_r}^{x_{r+1}}{(-1)^r.t(x)dx}} \ where \ x_0, ...

Integrate the foll. ∫ 12x12+5x9/x5+x3+1 dx ∫etanx(xsec2x + sin 2x )dx ∫e3x( 2+3sin2x/1+cosx )dx ...

Let a real function f(x) satisfy following conditions : 1)f(x+y+1)=(\sqrt{f(x)}+\sqrt{f(y)})^2 2)f(0)=1 3)f(x)\geq 0 \ \forall x\in R Find f(x) ...

1> \lim_{x\rightarrow 0}\frac{e^{-4x}-1}{e^{-2x}+e^{-x}-2} 2> \lim_{x\rightarrow -1^{+}}\frac{\sqrt{\pi}-\sqrt{cos^{-1}x}}{\sqrt{x+1}} 3> \lim_{x\rightarrow 1}(1-x)tan(\frac {\pi x}{2}) ...

f(x) = log { log|sin x|(x2-8x+23) - 3/log2|sin x| } Find the domain of this function. ...

1) ∫(tan(pi/4-∂))/sin∂cos∂√(1+tan∂+cot∂) d∂ = -2tan-1√f(∂) + c. Then Minimum value of f(∂) is Opts - 4, 2, 6, 3 2) f(x) and g(x) are two real valued functions. Find the no. of solutions of equation ∫f( ...

f:R→R be twice diff fn satisfying f"(x)-5f'(x)+6f(x)≥0 for all x≥0.If f(0)=1,f'(0)=0 and f(x) satisfies f(x)≥a.h(bx)-b.h(ax) for all x≥0,then find (a+b).h(0) i understood BT's soln...but i am looking for shorter met ...

1) limx→0 x2/sinx.tanx 2) limx→0[ x2/sinx.tanx ] 3) limx→0{ x2/sinx.tanx } 4)Find a,b i) limx→∞( x2+1/x+1 -ax-b)=0 ii) limx→∞( x2-x+1 -ax-b)≥0 ...

sum of the series \frac{1.2}{3!}+\frac{2.2^2}{4!}+\frac{3.2^3}{5!}+............\infty ...

Find the intervals of monotonicity of 1) sin\frac{\pi }{x} 2) (log_{3}x)^{2} + log_{3}x ...

sin2 nx ------------------ dx sin2 x ...

Q1 limx→0[ ex-1/x ] Q2 limx→0 { ln(1+x)/x } where [.] =GINT and {.} is fract part ...

what are many-many maps......plz give definiton and an example!!!!!! ...

let f(x) be a differentiable function satisfying (x-y)f(x+y)-(x+y)f(x-y)= 4xy(x2-y2) for all x,y belongs to R . f(1) = 1 then.... 1. the area of the region bounded by the curves y=f(x) and y=x2 is.... 2. the value of ∫-12 f ...

lim sin[cos x]/1+[cos x] x→0 where [.] is GIF.... ...

∫1/1+x^16 ...

*Image* MERA [3]UTTAR[ANSWER][3] 1 AA RAHA HAI.........PUSTAK MEIN SHUNYA[ZERO] DIYA HAI............KAUN SA UTTAR SAHI HAI!!!![3] ...

show the graph of *Image* ...