Recently Active Calculus Questions

q1)fna and gna exist and are not equal for some n . Further if f(a)g(x) - f(a) - g(a)f(x) +g(a) =4 g(x) - f(x) then value of n is: ans is 4 how?? lim ( 1+24+34+........n4 - lim 1+23+33+........n3 ) n→∞ n 5 Q2)expansion of ...

I don't know how to solve it, But I thought it will be nicer for those who know how to solve it : *Image* ...

The conditions of two functions being equal: (1)Ranges should be equal (2)Domains should be equal Now my doubt is, let one function be sinx and the other be cosx,then we have the ranges and the domains of both the functions t ...

along line y=x-1 is: Q2)lim(x→ ∞ ) [aoxm + a1xm-1 + a2xm-2 + ....+am-1x+am] [b0xn+ b1xn-1 + b2xn-2 + ...+bn-1 x +bn ] when a0b0 >0 is infinity when a0b0 <0 is - infinity Can someone pls explain how??? Q3)lim (x → ...

Find all local strict maximum of the function F(x) = 0, x irrational = 1/q,x= p/q in lowest terms ...

i hav a doubt in calculating curved area and volume of a cone . let height =h and radius of base = r , where tanθ = r/h now my doubt is : suppose vertex of cone is origin and height is along x axis then we can write curved a ...

*Image* Give a Detailed Solution ...

in calculating curved area and volume of a cone . let height =h and radius of base = r , where tanθ = r/h now my doubt is : suppose vertex of cone is origin and height is along x axis then we can write curved area = ∫2πy ...

f(x)=x+∫01(x2y+y2x)dy find f(1)(x and y are independent variables) ...

Limn→∞1/n(2.5.8.11........3n-1)1/n ...

evaluate the limit: \lim_{x\rightarrow \propto } \frac{x^{2}(1+sin^{2}x)}{(x+sinx)^{2}} ...

$If A= $\lim_{x \to \frac{\pi}{2}}\frac{1-sin^{\lambda+\mu}x}{\sqrt{(1-sin^\lambda x).(1-sin^\mu}x)}$\\\\ where $\lambda,\mu>0$, Then find $A=$ ...

Q1. \int_{0}^{\pi /2}{ln(a^2cos^2\theta +b^2sin^2\theta )d\theta } Q2. \int_{0}^{\infty }{\frac{ln(1+a^2x^2)}{1+b^2x^2}dx } Q3. If lxl < 1 then find the sum of the series \frac{1}{1+x}+\frac{2x}{1+x^2}+\frac{4x^3}{1+x^4}+\ ...

$Let $x_{i}=2^i$ and $i=1,2,3...........16$\\\\ Then find Min. of the function $f(x) = \sum_{i=1}^{16}|x-x_{i}|$ ...

$Calculate $\int_{-\infty}^{+\infty}\frac{1}{(x^2+x+1)^3}dx=$ ...

A curve is represented parametrically by the equation x= t+eat and y = -t + eat when t belongs to R and a> 0.. If the curve touches the axis of x at the point A, then the coordinates of the point A are 1. (1,0) 2 (1/e, 0) ...

[1] range of f(x)= *Image* is_______? ...

If f:[0,pi]→R is continuous and ∫(0 to pi) of f(x) cos x dx=∫(0 to pi) of f(x) sin x dx=0,then the number of roots of f(x) in (0,pi) is ___________? ...

f(x)=cos x/{[2x/pi]+0.5} where x≠integral multiple of pi,[.]=greatest integer function is f(x) even/odd/neither ...

if f(x)=√(x-m+1), for x in [m-1,m), m=integer,then evaluate *Image* where n=natural number. ...

$Calculate $\int_{-\frac{\pi}{2}}^{\frac{\pi}{2}}\frac{cosx-xsinx}{x^2+cos^2x}dx$ ...

Evaluate: \lim_{n\to\infty}\dfrac{1}{n}\sum_{k=1}^n\left(\left[\dfrac{2n}{k}\right]-2\left[\dfrac{n}{k}\right]\right) Here [x] represents the greatest integer less than or equal to . ...

this is a question from M.spivak *Image* ...

*Image* please solve this ...

lim 0 to 2Π∫ecosθcos(sinθ)dθ = ? 1) 2Π2) Π3) Π/2 4) none ...

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for a sufficiently large value of n the sum of the square roots of the first n positive integers i.e. √1 + √2 + .... √n is approximately equal to?? ...

(1) \lim_{x \to \frac{\pi}{4}}\frac{\sqrt{1-\sqrt{sin2x}}}{(\pi-4x)}=$ ...