Recently Active Calculus Questions

if f(X) = x + 0∫(1xy2+x2y)f(y)dy f(x) has minima at a)x=9/8 b)x=-9/8 c)x=0 d)x=1 ...

if g(x)=1/4 ( f(2x2 - 1)+1/2 f(1-x2 ) ) and f|(x) is an increasing function then g(x) increases on (subjective type) ...

1) ∫xtanx dx ...

\int_{1}^{\infty}{\frac{x^3+3}{x^6(x^2+1)}} = ? ...

let f :R-->R be any function . define g :R-->R by g(x) = |f(x)| for all x. then g is a. onto if f is onto b. one=one if f is one-one c.continuous if f is continuous d. differentiable if f is defferentiable any example o ...

\lim_{x\to 0}\left(x\sum_{i=1}^k\left[\dfrac{i}{x}\right]\right) = ?? Here [x] denotes the greatest integer function and k is a natural number. ...

if x ε R find maximum value of 2(a-x)(x+ x2+b2 ) any method other than dy/dx ?[7][7] ...

This is crackable but nice: f:(a,b) \rightarrow \mathbb{R} is continuous. Prove that given x_1, x_2, x_3,...,x_n in (a,b), there exists x_0 \in (a,b) such that f(x_0) =\frac{1}{n} \left(f(x_1)+f(x_2)+f(x_3)+...+f(x_n) \right) ...

WAT IS WALLI's FORMULA??? I guess it is some generalisation for \int_{0}^{\Pi /2}{sin^{2k}x\times \cos ^{2n}x}\, dx Can sum1 pl. tell me wat it is precisely.............. ...

the tangent to curve y=ex drawn at point (c,ec) intersects line joining the points (c-1,ec-1) and (c+1,ec+1) at the point????????????????? which is shortest posible method to solve this type of question????plz share ur ideas. ...

Like the title says, this is not JEE stuff, but if you have been following some of my recent posts, this may be worthwhile doing: \int_0^1 f(x) \ dx = \int_0^1 x f(x) \ dx = 1 Prove that \int_0^1 f^2(x) \ dx \ge 4 ...

i even dunno the answer.. from a variable point C on a circle a perpendicular is drawn on a chord AB of the circle meeting the chord at D.Then evaluate lim.(C→B ) CD2/DB ...

A is d area boundd by x=mod(y^2-1) and y=x-5 the 6A = ? ...

This thread features my doubts in integration problems.....others can feel free to post their own!!! OK HERE GOES: I came across these questions in Brilliant Tutorials Elite Course ...... (I) Both of the questions below have ...

For f continuous on \mathbb{R} , find the limit: \lim_{h\to 0}\dfrac{1}{h}\int_a^b \big(f(x+h)-f(x)\big) \mathrm{d}x Remember, f has been said only to be continuous and not differentiable. (rajat, dipanjan, metal: wait for at ...

Q1 \lim_{x\rightarrow 1}\frac{x^{x}-1}{xlogx}-\lim_{x\rightarrow 0}\frac{log(1-3x)}{x} ...

Inscribed in a circle of radius R is square,a circle is inscribed in the square,a new square in the circle and so on for n times.... Q1 Sum of areas of all circles Q2Limit of sum of areas of all squares as n→∞ Q3The limit ...

If \alpha =e^{2i\pi/11 } and f(x)=5+\sum_{K=1}^{60}{A_K{x^{K}}} then find value of 100\sum_{r=0}^{10}{f(\alpha ^{r}x}) ...

lim ax+bx+cx 2/x x→0 ______ 3 ...

*Image* ...

Can someone please give me the important properties of limits??? ...

These are all Kaymant (Anant) Sir's questions Q. Suppose f(x) be a real valued function defined for all x≥1 satisfying f(1) = 1 and f ' (x) = 1/[x2 + f(x)2] Prove that the limit of f(x) as x goes to infinity exists and is l ...

Let\ f:R^{+}\rightarrow R\ be\ a\ strictly\ increasing\ function\ such\ that\ f(x)>-\frac{1}{x}\forallx>0\\ And\ also\ f(x).f\left(f(x)+\frac{1}{x}\right)=1\\ \\ Match\ the\ following:\\ \\ f(1)=\\ f_{max}x\ in\ [1,2]=\ ...

∫1-sinx dx/x(1-x3e3cosx) ...

1. \int (sec^{2}x+sin^{2}x)/2sin^{2}xcos^{2}x 2. \int 1/x^{3}(x-1) dx 3. \int (1+x^{2}+x)/x^{2}(x+1)dx ...

can anyone help me out in finding limits by ε-δ method?? exams mein aa rahaa hai yeh sab... although simple limits hi hain.. ...

If f(x)is be periodic with period λ & f(-x)+f(x) =0 Prove that ax∫f(t)dt is periodic with λ ...

lim sin( x )/ x x→0+ ...

this is a passage question..........i solve d the rest of them but cant do this one..... A point is moving on curve S such that at any instant the slope is proportional to ratio of absicca with ordinate of point and area boun ...

THE AREA ENCLOSED BETWEEN y2=x AND THE LINE x+y=2. me getting 7/6+something/2 [266] [265] [264][262][269] ...