Recently Active Calculus Questions

I can find the domain and range when there is a case of composition of general function. But,I face difficulty in finding out the range and domain of real functions. Am posting some doubts, please help me out. 1)Let f be a re ...

in the case of the differential eq of all non-horizontal lines in a plane we take ax+by =1 and then differentiate it twice with respect to y , and in the case of all non-vertical lines in a plane we differentiate the above eq ...

if f: R-R is a function satisfying the property f(2x+3) + f(2x+7) = 2 for all x belongs to R , then the period of f(x) is ...

if y, = y+1 and y(0)=1 find value of y(ln2) ...

1 . Does there exist a function " f " defined on the set of positive real numbers which takes only positive real values , and satisfies , i > f ( x f ( y ) ) = y f ( x ) ii > f ( x ) tends to zero as " x " approaches in ...

0 ∫ 1 tan-1 ( 1-x + x2 ) dx ...

not much tough \int_{0}^{1}\frac{\ln(1+x)}{1+x^{2}}\mathrm{dx} ...

A Horse is at a point P at time t=0 Horse moves along the track at speed of 20 km/hr.How fast is his shadow moving on the wall when he has covered 1/8 of the track. *Image* ...

if f(x)=x3-3x+1 then fiind the number solution of f(f(fx)). plzzz do solve in detail nd explain how to solve.. ...

x2+y2 = aetan-1(y/x) , a>0 then y''(0) : a) a/2.e-π/2 b) aeπ/2 c) -2/a.e-π/2 d) none ...

1. If a(0) = x , a (n+1) = f( a ( n ) ) , n= 0 , 1 , 2 , ............................., find a(n) when (i) f(x) = root of (mod x ) (ii) f(x) = 1 / 1-x 2. Let f(x) be a real valued funcn defined for all real nos x such that fo ...

A point P moves inside a triangle formed by A(0,0), B(1,1/ 3 ), C(2,0) such that min{PA,PB,PC} =1, then the area bounded by the curve traced by P is.... (a) 3 3 - 3∩/2. (b) 3 + ∩/2. (c) 3 - ∩/2. (d) 3 3 + 3∩/2. i am n ...

Consider the polynomial f(x) = ax2+bx+c. If f(0) = 0 and f(2) = 2, find the minimum value of \int_{0}^{2}{\left|f'(x) \right|}dx equals?? i get 2a+b=1 (simple), but how to get the value of -b/2a?? ...

another quesn : 1. Let b not equal to 0 and for j = 0 , 1 , 2 , .........,n let Sj be the area of the region bounded by the y - axis and the curve xeay = sin by , j pi/b is less than equal to y is less than equal to (j+1) pi ...

1) Let R be a relation on N defined by x + 2y = 8. The domain of R is (a) {2,4,8} (b) {2,4,6,8) (c){2,4,6} (d) {1,2,3,4) . Give the reason to your answer. 2)The relation 'R' in NxN such that (a,b) R(c,d) <==> a+d=b+c. H ...

1)Modulus Function if a, b are positive real numbers,then x2 ≥ a22 <=> lxl ≥ a <=> x ≤ (-a) or x ≥ a. HOW x ≤ (-a) ? 2) Greatest Integer Function [x] > k => x ≥ k + 1, where k is an integer. Plea ...

Find all functions f: \mathbb{R}^+ \rightarrow \mathbb{R} , such that whenever x,y \in \mathbb{R}^+ , f(x+y) = f(x^2+y^2) [Note, no conditions of continuity, differentiability are given] ...

f(x) = [x]cos( 2x-1/2 ) pie , where [] is greatest integer is discontinuous at ?????????????? a) all x b) all integer points c) no x d) x which is not an integer e) at all I+ f) at all I- g) at (n)pie h) at (n-1)pie ...

THE EQUATION OF THE WICTH OF AGNESI CURVE IS:- y=8a3/ x2 + 4a2 or y=8a3 / x3 + 4a2 in another site i saw it as the first equation... bt in a sum of the integral calculas book of arihant the latter equation is given... or is i ...

1) If f : R→R is a continuous and differentiable function such that \int_{-1}^{x}{f(t)dt} + f'''(3) \int_{x}^{0}{dt} = \int_{1}^{x}{t^{3}dt} - f'(1) \int_{x}^{2}{t^{2}dt} + f''(2) \int_{3}^{x}{tdt} , then find the value of ...

If a funcn. f(x) is bijective in [a,b] , then prove that integral a to b f(x) dx + integral f(a) to f(b) inverse of f(x) dx = b f(b) - a f(a) ...

plz suggest me sum goodbok fr doin functions nd calculus fr jee ...

Q) Find f(x) if \int_{1}^{xy}{f(t)dt} = y \int_{1}^{x}{f(t)dt} + x \int_{1}^{y}{f(t)dt} ...

1. limn→∞ (4n+5n)1/n= 2. limn→∞ ( xn + yn )/(xn - yn ) where x>y>1 is equal to 3)limx→ - ∞ {√(x2 - x + 1) - ax - b} = 0. then (a,b) is equal to 4)lim x→0 (cos(sin x) - cos x)/x4 is equal to PLEASE SOLVE ...

the value of: lim [ |sin x|/|x| ] x→0 [.] represents greatest integer function |.| represents modulus.... ...

Passage For x ε (0 , Π/4), Let Sn = \sum_{r=1}^{2n}{sin(sin^{-1}x^{3r-2}}) Cn = \sum_{r=1}^{2n}{cos(cos^{-1}x^{3r-1}}) Tn = \sum_{r=1}^{2n}{tan(tan^{-1}x^{3r}}) 1) The correct order of Sn, Cn, Tn is 2) The value of \lim_{n\ ...

1 \int_{0}^{\infty }\frac{dx}{x^{n}+1},n=natural\: no ...

The period of mod(Sin2x) + mod(Cos2x) is........ isnt the answer pi/4 ???? ...

integrate the following: 1. sin inverse ( root of x / a+x) 2. root of ( 1+ lnx ) / x lnx 3. 1 / root ( 1 - sin ^ 4 x ) dont give the soln. just give the necess. hints.... ...

Q) \int ( \frac{1}{\sqrt[3]{x} + \sqrt[4]{x}} + \frac{ln( 1 + \sqrt[6]{x}}{\sqrt[3]{x} + \sqrt[]{x}} ) dx ...