Recently Active Calculus Questions

1) Show that the least natural number a for which x + ax -2 > 2 for all x belonging to (0,∞) is 2. 2) Let f(x) = sinx+ax+b, then show that f(x)=0 has (a)only one real root which is positive if a>1, b<0 (b)only one ...

if ∫ f(x) dx = i ( UL= b, LL=a) ∫ f( x - (1/x)) dx ( UL=b,LL=a) =? UL=upper limit LL=lower limit ...

Q1. y=sin^-^1(2x\sqrt{1-x^2}) then dy/dx = (Find answer by trigonometric substitution)? My attempt: Let x=sinθ Then the given expression translates to y=2θ = 2sin-1x So, dy/dx = 2/ 1-x2 Let x=cosθ Then the given expression ...

let a1,a2,......,an be a sequence of real numbers with an+1=an+(√1+an^2) and a0=0 find limit an/2^(n-1) n→∞ ...

Ques1) Show that one of the solution of the equation -x4+x2-P=0 where x belongs to (0,1) and P belongs to (0,1/4) is sin (1/2 sin - 1 2 √P). Ques2) Tangents are drawn to y = ax2+bx+c at (5,4) is parallel to x- axis. If a be ...

integrate: ∫1/1+x^n ...

Ques1) Show that the value of ∫ [(1 - cot n-2 x) / (tanx + cotx .cot n-2 x ) ]dx is equals to (1/n) log | sin n x + cos n x| + c. Ques2) If I1 =∫ sin -1 x dx and I 2 = ∫ sin -1 1-x 2 dx then show that I 1 +I 2 = pie x / ...

Q1. \int (cos2\theta )^3^/^2cos\theta d\theta Q2. \int \frac{cos8x-cos7x}{1+2cos5x}dx ...

If f(x+y)=f(x)+f(y) where x,yε R and ∫(0 to 1) f(x).dx=1 find f(1) ...

what is the reduction formula for ∫ 1/1+x^n ...

f(x+y)=f(x)+f(y) where x,yεR Prove thta nf(x-\frac{a}{n})+f(a) is an odd functionm wheere nεI-{0} I am also givng ma soln...plz continue and finsh it off... nf(x-a/n)=+f(a) =>nf(x)-nf(a/n)+f(a) =>nf(x)-n(f(a/n)-1/nf(a ...

If area bounded by y=logx,y=x ,x2+y2+2xy-k2=0 is a square units,then calculate area bounded by y=ex,y=logx ,x2+y2+2xy-k2=0 . ...

Find the minimum value of \frac{a^2}{cos^2x}+\frac{b^2}{sin^2x} ...

All points on the curve y2=4a(x+asin(x/a)) at which the tangents are parallel to the X axis lie on which curve ? I solved it and got x=aπ But answer is a parabola Please give the right solution :-) ...

I_1=\int_{0}^{1}{e^{-\frac{x^2}{2}}}dx I_2=\int_{0}^{1}{e^{-x^2}}dx I_3=\int_{0}^{1}{e^{-x^2}}cos^2xdx I_4=\int_{0}^{1}{e^{-x}}cos^2xdx ...

Let g'(x)>0 and f'(x)<0 for all x ε R then prove that g(f(x+1))<g(f(x-1)) ...

One problem that has been troubling me for ages now.. anyone who can try and solve? ∫(tan x)1/6 dx ...

Evaluate the following limit: \lim_{x\to+\infty}\left(\sqrt[n]{(x+2)(x+4)\cdots(x+2n)}-\sqrt[2n]{(x+1)(x+2)\cdots(x+2n)}\right) where n is a positive integer. ...

\int_{0}^{\infty}{e^{-x^2}dx}=\sqrt{\frac{\pi }{2}} then find value of \int_{0}^{\infty}{e^{-ax^2}dx},a>0 ...

Find f(x) if \int_{0}^{a}{f(x)dx}=\frac{6a-sin2a}{4};a>0 ...

Ques1) Show that the extremum value of the function f(x) = 1 / (sinx+4) - 1 / (cos x -4), where x belongs to R is 2 2 / (4 2 + 1). Ques2) If a2x4 + b2y4 = c6, then show that the max value of xy is c3 / 2ab . Ques3) If x7 - x5 ...

If tan^{-1}(x+h)=tan^{-1}x+(hsiny)(siny)-(hsiny)^2.\frac{sin2y}{2}+(hsiny)^3.\frac{sin3y}{3}+..........\infty if x\epsilon (0,1),y\epsilon (\frac{\pi }{4},\frac{\pi }{2}) then y = ? ...

\int_{-1}^{1}{\frac{sinx-x^2}{3-[x]}}dx ...

For some g,let f(x)=x(x+3)eg(x) be a continuous function. If there exists only one point x=d such that f'(d)=0,then find interval in which d lies. ...

f(x)=sin(x-a)/sin(x-b) Find prove that f(x) assumes maximum or minimum values for a-b=nπ ,n ε I ...

\lim_{x\rightarrow 0}\int_{0}^{x}{\frac{t^2dt}{(x-sinx)\sqrt{a+t}}}=1 ...

Perform the following integration: \int\dfrac{\mathrm dx}{1+x^4} ...

http://targetiit.com/iit-jee-forum/posts/solve-this-10617.html can anybody explain nishant byah explanation here ...

find the are area bound by a2x2=y3(2a-y)and y-axis ...

Ques1) The eqn of tangen to the curve y = cos(x+y) where -2pie ≤ x ≤ 2 pie, that are parallel to the line x+2y = 0 (a) x+2y = pie/2 and x+2y = -3 pie/2 (b) x+2y = pie/2 and x+2y = 3 pie/2 (c) x+2y = 0 and x+2y = pie (d) n ...