Recently Active Calculus Questions

1) \ f(x)\ is\ a\ polynomial\ of\ degree\ 4\ with\ real\ coefficients\ such \that\ f(x)\ =\ 0\ is\ satisfied\ by\ x\ = \1,2,3\ only\ , \ then\ f ' (1). f'(2). f'(3)\ is\ equals\ to \ \\\\\ (a)\ 0\ (b)\ 2\ (c)\ -1\ (d)\ none\ ...

$Determine The no. of real roots of the equation $(2^x+x-1).(x-3)=-2$ ...

Prove that 1)Limx--->0 loge(1+x)/x = 1. 2)Limx-->0 ax-1/x = logea, a>0,a≠0. In the second one,its 'a' to the power 'x' minus 1 divided by 'x' to give log 'a' to the base 'e'. ...

lim n→∞ (an + bn)(1/n) ...

(2) $Calculate $\int\frac{(x^2-1)}{x.\sqrt{x^2+\alpha x+1}.\sqrt{x^2+\beta x+1}}dx$ ...

Find all continuous functions f, g, h : R → R for all real values of x and y satisfying the functional equation f(x + y) = g(x)+h(y) . ...

If f be a periodic function as well as an odd function with period p and and x belongs to [ -p/2, p/2] Prove that ∫f(t)dt (lower and upper limits are a and x resp.) is periodic with period p. In the solution, there is a ste ...

1) Find the domain of f(x) = cos^{-1}\sqrt{log_{[x]}(\left|x \right|/x)} ...

1. \int \frac{dx}{tanx+secx+sinx+cosx+cotx+cosecx} 2. U_{n}=\int_{0}^{1}{x^{n}\left(2-x \right)^{n}dx}, V_{n}=\int_{0}^{1}{x^{n}\left(1-x \right)^{n}dx} ; prove\ \right| that\ \right| U_{n}=2^{2n}V_{n} ...

1) prove \lim_{x\rightarrow 0} sin x / x =1 by squeeze theorem. 2)prove that all roots of e^x [ d^n/d x^n(x^n/e^x)] are positive 3) prove that e is irrational. ...

Draw the graph of f(x)=x+1/x ...

\int\frac{cos7x-cos8x}{1+2cos^2x}dx ...

Prove that \int_{0}^{n\Pi}{\left|\frac{sinx}{x} \right|}dx < \frac{2}{\Pi}\left(1 + \frac{1}{2} + \frac{1}{3} + ......\frac{1}{n} \right) ...

\int_{0}^{\frac{\Pi }{2}}\frac{dx}{1+cos^{2}x} In arihant, he divides Nr and Dr by cos2x which is absurd as it would be like dividing by 0 as cos2(90) =0 (90 is in the domain of x) Secondly, after this step, the integrand is ...

Evaluate \int_{-1}^{0}\frac{dx}{x^{4}-x^{2}+1} ...

$Calculate $\int_{\frac{1}{2}}^{2}\frac{1}{(x^2-3x).(x^{2010}+1)}dx$ ...

prove that ∫01xxdx =Σ∞n=1 (-1)n+1/nn how to proceed ? ...

Post some questions based on RANGE DOMAIN and functional equations! Thank u ...

i have open this thread to discuss integration questions ... so post questions and we will discuss it........... ...

f(x) = sinx -x find area bounded by y=f-1(x) ,tangent and normal drawn to it at the points with abscissae π and 2π . ...

\lim_{n \to \infty }n.sin(2\pi en!)= ...

$\underline{\underline{Q:}}\Rightarrow $\lim_{x \to\0}\ \frac{sin(tanx)-tan(sinx)}{sin^{-1}(tan^{-1}x)-tan^{-1}(sin^{-1}x)}= ...

What is \huge \lim_{n \rightarrow \propto }\frac{x^{n}}{n!} ????? ans : 0 (Right now I am studying in a state engg colg. in 1st yr. I came across this qsn once in success magnet of Aakash Inst. and another time while the teac ...

Let f(x) =(x-1)p.(x-2)q where p,q>1. Each critical point of f(x) is a point of extremum when - (Options are given) I got the critical points as 1 and 2. I don't know what do I do next. I found the second derivative but I t ...

Please explain range........with some moderate examples from the basics Thnk u Shubham ...

lim cos(pi√(n2 + n)) n→∞ ...

$Q:$\Rightarrow$ Find value of $x$ which Satisfy The equation [x[x]]=1$\\\\ $Where $[x]$ Denote Greatest Integer function. ...

How do we find the next term in these series? I mean what is the logic behind every successive term? *Image* *Image* It is not an AP or GP. Please help ...

How do we find the next term in these series? I mean what is the logic behind every successive term? *Image* *Image* It is not an AP or GP. Please help ...

the equation a + (a^2-2a-8)x = x^3 has only one real root? what is the possible range of a? ...