Recently Active Calculus Questions

How to solve this one? value of lim x->0 loge(sinx)^tanx ...

lim (n→∞) tan2nx is equal to A) 1 if x = 2nπ + π/4 B) 1 if x = nπ + π/4 C) 0 if x ≠nπ + π/4 D) 0 if nπ - π/4 < x < nπ + π/4 There may be more than one option correct ...

Let f(x) be the monotonic polynomial of (2m-1) degree where m belongs to natural no., then equation f(x)+f(3x)+f(5x)+. . . . . .f((2m-1)x) = 2m-1 has: A) At least one real root B) (2m-1) real roots C) exactly one real root D) ...

f(x)= |x2n+1|, n belongs to N then, A) f(x) is continous but not differentiable at x=0 B) f(x) is differentiable at x=0 C) f(x) is discontinous at x=0 D) none of these. ...

If a1<a2<a3<a4<a5<a6, then equation (x-a1) (x-a3) (x-a5) + 3(x-a2) (x-a4) (x-a6)=0 has: A) three real roots B) a root in (-∞,a1) C) no real root in (a1,a2) D) no real root in (a5,a6) There may be more than on ...

∫dx 1/sinx + cosx ∫ x2/√1+x3 ∫ sec7x-7/sin2x ∫(1+cot(x+α)cot(x-α)) dx ∫ log(cosx)/cos2x ex-1/(x2-5x+4) please try them! ...

*Image* ...

\mathbf{(1)\;\;\int\frac{1}{\left(\sec x+\csc x+\tan x+\cot x\right)^2}dx} \mathbf{(2)\;\int_{0}^{\pi}\left\{\mid \sin (2010x)\mid}-\mid \sin (2011x)\mid\right\}dx$ ...

x2+x3≤x+f(x)≤x5-x3 , for value of x near 0, f(x) is: A) -1 B) 0 C) 1 D) none of these ...

find the integration ......... ∫sin(sin(sin(sin(..........∞........(sinx)))..........)) dx ...

This is a dig from the old threads of TargetIIT which was unsolved. Let f be a continuous function in [a,b]. Prove that there exists c \in \left(a,b \right) such that \int_{a}^{c}{f(x)dx}=\left(b-c \right)f(c) . ...

\int_{\frac{\pi}{6}}^{\frac{\pi}{3}}\frac{1}{\sin^2 x.\sin\left(x+\frac{\pi}{6}\right)}dx=$ ...

1. Let f be defined on [0,1] be a twice differentiable function such that, \left|f''(x) \right|\leq 1 for all x \in \left[0,1 \right] . If f(0)=f(1) , then show that, \left|f'(x)\right|<1 for all x \in \left[0,1 \right] . ...

In mathematics, the Gamma function (represented by the capitalized Greek letter Γ) is an extension of the factorial function to real and complex numbers. For a complex number z with positive real part the Gamma function is d ...

find greatest integer of the following 1/ 2 +1/ 3 +1/ 4 +.............+1/ 80 ...

\hspace{-16}$Calculate value of \\\\\\ $\mathbf{(1)::I_{1}=\int_{0}^{\pi}\frac{\sin x}{7+4\cos 2x+\cos^2 2x}dx}$\\\\\\ $\mathbf{(2)::I_{2}=\int_{0}^{\pi}\frac{x.\sin x}{7+4\cos 2x+\cos^2 2x}dx}$\\\\ \hspace{-16}$Ans\; :: $I_{ ...

\hspace{-16}\int\frac{x^2}{\left(1+\sin 2x\right)}dx ...

Solve 1 +x2 +y2 +x2 y2 + xy dy/dx = 0 ...

Q. Let f(x) and g(x) be differentiable functions such that f'(x)g(x)\neq f(x)g'(x) for any real x. Show that between any two real solutions of f(x)=0 , there is atleast one real solution of g(x)=0 . ...

\hspace{-16}$If $\mathbf{f(x)}$ is a defined function in such a way such that\\\\\\ $\mathbf{f(x+1)=\frac{f(x).\cos\left(\frac{\pi}{67}\right)+\sin\left(\frac{\pi}{67}\right)}{\cos\left(\frac{\pi}{67}\right)-f(x).\sin\left(\f ...

*Image* ...

Integrate: 1) ∫ 1/sinx+sec x dx Please show me the steps also. ...

let f1(x) = x for 0≤x≤1 1 for x>1 0 otherwise and f2(x) = f1(-x) for all x f3(x) = -f2(x) for all x f4(x) = f3(-x) for all x Which of the following in necessarily true? 1. f4(x) = f1(x) for all x 2. f1(x) = - f3(-x) fo ...

\int_{-\infty}^{\infty}{\left|Axe^{-x^2/2} \right|^2}=1 ...

∫ee+ee+ee+xdx Where 'e' is the exponential function ...

1∫2|x2|dx ...

evaluate ∫ x4/1+x4 dx ...

\hspace{-16}$\textbf{For what real value of $\mathbf{k}$ for which the equation}\\\\ $\mathbf{x^3-2x^2-2010x+k=0}$ \textbf{has no Real solution.} ...

suppose *Image* now method 1, L=\lim_{x\rightarrow \propto } \frac{1-sinx/x}{1+sinx/x} since (sinx /x) →0 L=1 now method 2, using L Hospital rule ( for ∞/∞ form) , L=\lim_{x\rightarrow \propto } \frac{1-cosx}{1+cosx} L= ...

* 1. Using the relation 2(1-\cos x)<x^2, x\neq 0 , or otherwise, prove that \sin(\tan x)\geq x, \text{ } \forall \text{ } x\in\left[0,\frac{\pi }{4} \right] . 2. Find the point on the curve 4x2+a2y2=4a2, 4<a2<8 that ...