Frequent Calculus Questions

1) show that the normal at the point (3t , 4/t ) of the curve xy = 12 cuts the curve again at the point whose parametr t1 is given by t1 = -16/9t3 ...

If f(x)=(sin3x+Asin2x+Bsinx)/x5. when x is not equal to 0. Find A and B given that the function is continuous at x=0 and also find f(0)! ...

A circle which contain a quadrelateral of maximum area and this quadralateral is contain a triangle of maximum area..IF triangle has its side of 4cm. Then find out all side of quadralateral and diameter of circle. ...

which one is greater: A=20104019 or B=2009200920112011 ...

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1.\int_{0}^{x}[1+t]^{3}dt 2.\int_{0}^{x}[x]dx plz help sir ...

find the order and degree of the differential equation if its solution is (y+c)^2=xc ...

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evaluate *Image* answer given is π2. ...

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{} is fractional func [] is GIF | |is mod *Image* 5. ∫(0 to x)ex-[x]d{x} 6. ∫(0 to 4){ x }dx 7.∫(-5 to 5)min({x+1},{x-1})dx ...

consider the integrals *Image* let I be the greatest among them. prove that I=I4 ...

1) Let f:R to R be continuous function which satisfies f(x)=∫(0 to x)f(t)dt, then the value of f(ln5) is: a)0; b)2; c)4; d) 6. 2) Let I=∫(0 to 1) (sinx)/ x and J=∫(0 to 1) (cosx)/ x .Then which is true? a)I<2/3 and J ...

Let f(x) be a non constant twice differentiable function defined on (-∞,∞) such that f(x)=f(1-x) and f'(1/4)=0.Then a) f''(x) vanishes at least twice on [0,1] b) f'(1/2)=0 c) ∫(frm -1/2 to 1/2)f(x+1/2)sinxdx=0 d) ∫(fr ...

Integrate:: 4x3[d2/dx2(1-x2)5]dx from 0 to 1.Here d2/dx2 means the double derivative of the function w.r.t.x. This sum is meant for students only ,not for experts. ...

If x>0 then integrate (2x-[2x])2 from 0 to 100[x] where [.] means G.I.F. ...

1) Prove that ∫x3 2ax-x2 dx=7πa5/8. 2) Integrate: [ x4/(1-x4)] *cos-1(2x/(1+x2). Upper limit=1/ 3 ;Lower limit=-1/ 3 . 3) Integrate::: 2-x2/[(1+x) 1-x2 ].Upper limit=1;Lower limit=0. 4) Integrate:::: log(1+tanx) from 0 to ...

∫ dx/cosx + cosec x ∫ 3cot3x - cotx/tanx - 3tan3x ∫tan{x -k}tan{x+k}tan2x ...

∫√(sin x-sin3x/1-sin 3x)dx ...

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2^sinx+2^cosx>1 ...

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∫(x3m+x2m+xm)(2x2m+3xm+6)1/mdx .For any natural no. m, x>0. ...

∫sec2x/(secx+tanx)9/2 ...

INTEGRATE: 1) (x3+3)/x6(x2+1). Upper limit=∞;Lower limit=0 2) xe-x/( 1-e-2x ). Upper limit=0;Lower limit=∞. 3) If f(x) be a function satisfying f'(x)=f(x) with f((0)=1 and g be the function satisfying f(x) + g(x)=x2,then ...