Recently Active Calculus Questions

For the curve y = x^2, shortest distance from variable point (0,c) to the curve is described by 'd' = f(c) where c belongs to R and d belongs to [0,∞) then f(c) (a) one-one, onto (b) many-one, onto (c) many-one, into (d) on ...

1) (a doubt) If f(x) = x2sin 1/x , x≠0 x, x=0 then find f'(0) if it exists... 2) (not a doubt) Given f(x) = |x| and g(x) = |x3|. Do the derivatives, f(0) and g'(0) exist? Explain!! :P please give detailed solution for the f ...

Evaluate: lim {x}/tan{x} x-->0 ...

X= 4SIN4X + SIN22∂ + 4 COS2{ PIE/4 - ∂/2 } AND PIE<∂ < 3PIE/2 .... FIND THE VALUE OF X...... ...

$Q:$\Rightarrow$ Find the least positive Integral value of $a$ for which the equation\\\\ $3x^4+4x^3-12x^2+5a=0$ has no real roots. ...

$Q:$\Rightarrow$ Find Max. value of The Expression $f(x,y)=x^2y-y^2x$\\\\. Where $0\leq x,y\leq1.$ ...

$Q:$\Rightarrow$ Find Range of $f(x)=\frac{x+2}{x^2-8x-4}.$ ...

1) Solve Limx→0[(1-ex) sinx/|x| ] ,where[.]represents greatest int func (A)-1 (B)1 (C)0 (D)None of these 2) Solve limx→ π/2 sinx -(sinx)sinx/1-sinx+logesinx ,(here x→ pi/2) (A)2 (B)0 (C)-1 (D)1 Pls solve!!! ...

If 0≤x≤100 , then total number of integer values taken by the function [x] + [2x] + [3x] + [4x] + [5x] is. ...

*Image* ...

1) If f( x+y/2 ) = f(x) + f(y)/2 for x,y belongs to R anf f'(0) exists and equal to -1 and f(0) = 1 then the value of f(2) is 1) 0 2) 1 3)-1 4) 2 answer 3 ---------------------------------------------------------------------- ...

I m new here & dis is my 1st post So help me out.Some of these probs mite b vry easy fr u guys & nt of IIT level bt stl pls solve them.Give suitable xplanations. 1) If f is an odd function and limx→0f(x) exists then limx→ ...

*Image* Integrate(xb-1 - xa-1)dx / 1-x, Limit {0 , Infinity} and 0<a,b<1. ...

Help me find the domain of the following functions. 1)f(x) = √(x2 - l x l - 2) Here am getting 2 cases when x≥0 and x<0, for x≥0 am getting the value of x as x≥2 and for x<0 am getting x≥-2 and x≥1, please t ...

lt from (-1 to 3/2) ---∫ IxI + Ix+2I + Ix+4I .dx where I I is modulus.... can we do it by breaking of limits or some other method??? ...

let a, b be the distinct positive roots of the equation tanx = 2x then evaluate ∫(sin(ax).sin(bx)) dx independent of a and b. lower limit = 0 upper limit = 1 ...

for any funtion y, dy/dx = (x - a)2n(x - b)2n+1 then a) a and b r point of minimum b) a and b r point of max. c) a is point of min and b is point of max d) a is point if max and b is point of min e) none of above ...

If y=e^x sinx Find d10y/dx10. ...

lim cos(pi√(n2 + n)) n→∞ ...

indefinite integration ∫ 0 = ??????????????? ...

\ \boxed{2}\,\,\, find\,\,\, f^{100}\left ({e}^{x^{2}}\right ) Fn(x) denotes nth derivative ...

is 1st order nd higher degree diffrntial eqtns(eg Clairaut's eqn nd all) in jee syllabus???? ...

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∫ x2 + 20 / (x sin x + 5 cosx )2 ...

Q>The equation f(x)=0 has 8 distinct real solutions & f(4+x)=f(4-x) then sum of all 8 solutions of f(x)=0 are- a>12 b>32 c>16 d>15 Please describe the solution. ...

*Image* In the given fig. graph of y = p(x) = x4 + ax3 + b2 + cx + d is given. If p(x) + c = 0 has 4 distinct real roots α , β , γ , δ then [α] + [β] + [γ] + [δ] is equal to (A) -1 (B) -2 (C) 0 (D) 1 plzz give the ful ...

In a circle with center O , OA , OB r radii angle AOB = 90 degrees . A semi circle (S1) is constructed using segment AB as its diameter non - overlapping with triangle OAB . The ratio of the area of S1 outside given circle to ...

find Min. and Max. value of r in 5r2 + 12r.cos(a) + 7 = 0 (where r ≥0) ...

\lim_{x\rightarrow 0} \frac{sec 4x-sec 2x}{sec3x-secx} ...

1) Let f: R→ R satisfy xf(x) = [x] f ({x}) + {x} f ([x]), (brackets have their usual meaning). Find f(x). ...