Recently Active Calculus Questions

\hspace{-16}(1)\;\;\mathbf{\int\frac{1}{x^{11}-8x^5}dx}$\\\\\\ $(2)\;\; \mathbf{\int\frac{5x-x^5}{x^8+1}dx}$ ...

find the derivative of x^x with respect to e^x^x. ...

\hspace{-16}\mathbf{\lim_{x\rightarrow 0}\left[\frac{(1+4x)^{\frac{1}{x}}}{e^4}\right]^{\frac{1}{x}}} ...

\{a_n\} is a sequence of real numbers such that |a_n- a_{n+1}| \le 1 \ \forall \ n \in \mathbb{N} Define b_n = \frac{a_1+a_2+...+a_n}{n} Prove that |b_n-b_{n+1}| \le \frac{1}{2} ...

Q. If y=\frac{1}{1+x^{n-m}+x^{p-m}}+\frac{1}{1+x^{m-n}+x^{p-n}}+\frac{1}{1+x^{m-p}+x^{n-p}} , then \frac{dy}{dx} at e^{m^{n^{p}}} \text{(a) }e^{mnp} \text{(b) }e^{\frac{mn}{p}} \text{(c) }e^{\frac{np}{m}} \text{(d) } none ...

Tangent lines to the curve : y=∫2|t|dt (limit from 0 to x) whch are parallel to the bisector of the first cordinate angle is given by? ...

\hspace{-16}\mathbf{\int_{1}^{\infty}\frac{x^2-3}{x.(x+1).(x^2+1)}dx} ...

\hspace{-16}(1)\;\;\mathbf{\int_{0}^{\pi}\frac{x^2\cos^2 x-x\sin x-\cos x-1}{(1+x\sin x)^2}dx}\\\\\\ (2)\;\; \mathbf{\int\frac{1}{x^n+x}dx}\\\\\\ (3)\;\;\mathbf{\int\frac{1}{1+\sqrt{x}+\sqrt{x+1}}dx} ...

*Image* \hspace{-16} $The aera of an equilateral triangle $\mathbf{OPQ}$ is bisceted by a curve $\mathbf{AB}$ of\\\\ minimal length. What is the equation of the curve with respect to\\\\ the given axes? ...

Q. Use the fact that e^x>1+x to prove that e^\pi>\pi^e . ...

Title: Arihant Differential calculus Problem DOUBTS Question Details:Attachments In Differential Calculus by Arihant Publication Pg.no. 88 - Q.no. 2,3,5 Pg.no. 90 - Q.no. 15,17 Pg.no. 91 - Q.no. 29 FOR THOSE WHO DONT HAVE THI ...

∫dx/(1+√x)^2010= 2[1/alpha(1+√x)^alpha - 1/beta(1+√x)^beta] +c where alpha, beta >0 A)|alpha-beta|=1 B)(beta+2)(alpha+1)=20102 C) beta and alpha are in A.P. D)alpha+1=beta+2=2010 ...

\hspace{-16}(1)\;\;::\int\frac{xe^x.(4+4(\cos x+\sin x)+\sin 2x)}{(1+\cos x)^2}dx\\\\\\ (2)\;\;::\int\frac{(4\sin x+3\cos x+\cos 3x)}{(2+\sin 2x)^2}dx ...

1) Find the range of sin2x + sinx - 1/sin2x - sinx + 2 2) Find range of cosx(sinx + \sqrt{sin^{2}x+sin^{2}\alpha }) ...

1) Find the set of values of a for which the function f(x)=x3+(a+2)x2+3ax+5 where f: R→R is one-one. 2) Find the condition for f(x)=ax3+bx2+cx+dsinx to be always one-one. ...

1) ∫(tanx)dx/(1-sinx) ...

please solve the following differential equation : dy/dx = 2y2 cosx+ y sin2x+2cosx sin2x/sin2x ...

∫[sinx + [2x/pi]] dx from pi/4 to pi/2 ...

\mathbf{\int\frac{\left(x-\sqrt{x^2+3x+2}\right)}{\left(x+\sqrt{x^2+3x+2}\right)}dx}$ provide complete solution. ...

for a given constant perimeter which of the following triangles will have max area? a)equilateral b)right angled c)scalene d)isosceles? i thought about it that by symmetry ,ans. will be a),but how do we numerically prove it?p ...

If f'(x2 - 4x + 3) > 0, then interval on which f(sin x) is increasing? ...

*Image* *Image* ...

Let A={1,2,3,4} B={a,b,c} Find the number of functions from A to B which are not onto. A.45 B.64 C.81 D.41 ...

Prove that point of discontinuity of the function f(x) = lim(x→∞) (2 sin x)2n/[3n - (2 cos x)2n] is nπ ± π/6 ...

1) Is 1∞ = 1 or it is not defined? 2) Also what about 2∞, 3∞ etc. ? ...

\hspace{-16}\mathbf{(1)\;\;\int_{0}^{1}\frac{1-2e^x\sin x}{(e^x+\cos x).(e^x+\sin x)}dx}$\\\\\\ $\mathbf{(2)\;\;\int\frac{1}{(x+1)^5.\sqrt{x^2+2x}}dx} ...

SOLVE 1. dy/dx = x/(2y+x) 2. (x2+y2)dy/dx= 8x2-3xy+2y2 ...

f(x) = -x3-9x2 + 24x + c has three distinct roots p,q,r now for c belongs to (-18,-16). the value of +[q]+[r] = ? where [k] represents greatest integer less than or equal to k ...

(x2+cos2x)/1+x2 integrate the above function.. PS- i already have done it, but the answer is not matching...a detailed solution is needed to check where i went wrong... ...

f(x+2) -5f(x+1) +6f(x) = 0 , f(0)=0 , f(1) = 1 then least positive prime factor of f(2008) = ? answer 5 ...