Recently Active Calculus Questions

∫(t-√(x2-1)/t+-√(x2-1) )dx ...

∫(sec2x/(secx+tanx)5)dx ...

Evaluate: \lim_{x\rightarrow 0} \frac{tan^{-1}x}{sin^{-1}x} ...

Let us consider a real valued function f:R --->R f(x+y) = f(x) + f(y) + f(x)f(y) , x,y ε R The sum and difference of two continuous/differentiable functions is also continuous (differentiable) over their common domain. Us ...

∫ tan-1x/1+x [lower limit 0 and upper limit 1]= (pi ln2)/k find k ...

if f(x) nd g(x) r twice differentiable functions on [0,2] nd if f''(x) = g''(x) nd f' (1) =4 , g' (1)=2 nd f(2)=3 , g(2)=9 then find g(4)- f(4)?? ...

given g(f(x))=x.then f(x) is one-one/onto/both/one one but not necessarily onto ...

IS TEHRE ANY METHOD TO SOLVE THE integrals OF THE FORM \int_{a}^{b}{\frac{px + q}{asinx + b cosx}} ...

If f(x) is continous in R and is symmetrical abt the lines x=1 and x=2 then which of the following holds. a)f(1+x)=f(x) b)f(x+3)=f(x) c)f(x+2)=f(x) d)none of these. pls explain.i know this will be a two liner but i am not get ...

wht is the Geometrical interpretation of the integration by parts formula???? plz give explaination ...

let f(x) be a quadratic polynomial with +ve integral coefficients and such that for every real a,b when b>a a∫b f(x)>0 also g(x)=f''(x)f(x) and g(0)=12 then a.total no. of quadratic polynomial is_____ b.f(x)=0 has rea ...

1) Area bounded by the curves y 2 (2a-x) = x3 and the line x=2a is (a) 3∩a2 (b) 3∩a2 / 2 (c)3∩a2/4 (d) none of these 2)Area included between the parabola Y = x2 / 4a and the which of the Agnesi Y = 8a3/x2 + 4a2 is (a) a ...

If the percentage error in measuring the surface area of a sphere is x%,then find the error in its volume. ...

The value of ∫-20 [x3+3x2+3x+3+(x+1)cos(x+1)]dx is (a)0 (b) 3 (c) 4 (d) 1 ...

PARAGRAPH : f(x) = ex / x decreases & increases respectively in (-∞,0) U (0,1) & (1,∞) respectively 1 ) Then what r the no. of solutions of ex = 2x ? A) 0 B) 1 C) 2 D) >2 2 ) The no of solutions of ex - 3x = 0 & ex + 3 ...

lim (1+ 1/a1 )(1+ 1/a2 )(1+ 1/a3 )....(1+ 1/an ) n→∞ where an is an=n(1+an-1) ; a1=2 ...

the least natural number 'a' for which x + \frac{a}{x^2} > 2 for all x \epsilon (0,infinity) is (a) 1 (b) 2 (c) 5 (d) none ans= (b) plz explain how? ...

(1)if f'(0)=0 and f(x) is a differentiable and increasing function then \lim_{x\rightarrow 0}\frac{xf'(x^{2})}{f'(x)}= (a) is always 0 (b) may not exist as LHL may not exist (c) may not exist as RHL may not exist (d) RHL is a ...

find the equations of tangents to the curve y2-2x3-4y+8=0 from the point (1,2) ...

Consider the differentiable function f(x) defined implicitly by the eqn y^3-3y+x=0 in the interval (-\propto ,-2)\bigcup{(2,\propto) } Given f(-10\sqrt{2})=2\sqrt{2} find f''(-10\sqrt{2}) ... A small hint will do....i mean wi ...

plz scroll down ...

find the value of *Image* ...

in a book there is some formula if f(x+y)=f(x)+f(y) then f(x)=xf(1).how does this come?? ...

This is another question from Larson's book.. .(Today I have given 2-3 from it) I_n=\int_{0}^{\pi/2}{\sin^nx dx} Show that I_{2n}=\frac{1.3.5....(2n-1)}{2.4.6....2n}\times \frac{\pi}{2} and I_{2n+1}=\frac{2.4.6....(2n-2)}{1.3 ...

∫0∞xeaxdx(limits from 0 to ifinity) ...

\int_{0}^{1}\frac{dx}{2+\sqrt{1-x}+\sqrt{1+x}} Solve :) ...

If f(0)=f(1)= 1/2 ,|f'(1)|<1 and f'(0)=2,then \lim_{x\rightarrow 0} \frac{f(sin x)-f(cos x)}{x} is A. 0 B. 1 C. 2 D. 1/2 ...

The integer n for which \large \lim_{x\rightarrow 0} \frac{(cos x -1)(cos x - e^{x})}{x^{n}} is a finite non-zero number is A. 1 B. 2 C. 3 D. 4 ...

Let f(x) = ax^2+bx+c be such that |f(x)| \le 1 \ \forall \ x \in \[-1,1] Prove that |2ax+b| \le 4 \ \forall \ x \in [-1,1] This topic is current in mathlinks.ro, and in any case no borrowed solutions please. ...

1) The no. of points at which the function f(x) = max {a-x , a+x, b}, - ∞ < x < ∞ , 0 <a < b cannot be differentiable is: (a)2 (b) 3 (c)1 (d) 0 2) If f(x) = sin (2∩ [ ∩2 - x] )/5 +[x] 2 ; where [.] denotes ...