Recently Active Calculus Questions

41. The value of ∫ {x .tanx . secx }/(tanx-x)2 In the answer key answer is given as A...whereas i think it should be B???????????? ...

Here is an interesting one x+x+x+x.......x times..=x2 diff. both sides w.r.t x 1+1+1..x times=2x x=2x 1=2 ...

differential coefficient of sin-1(3x-4x3) w.r.t. sin-1x is : a) 3 if -1 ≤ x ≤ 1 b) -3 if -1 ≤ x < -0.5 c) 3 if -0.5 < x < 0.5 d) -3 if -0.5 < x ≤ 1 ...

1. ∫ (cos 5x +cos 4x) / (1- 2 cos 3x ) dx 2. ∫ ( cos3 x ) . x. elog(sin x) .dx 3. ∫ ( x + ( x 2 ) + 2. x1/6 ) / [ x. { 1+ x } ] ...

The equation of a curve is y = f(x). The tangents at (1, f(1)), (2, f(2)) and (3, f(3)) make angles π/6 , π/3 and π/4 respectively with the positive direction of the x-axis. Then the value of 23∫f'(x).f"(x).dx +13∫f"(x ...

Can anyone plz explain the use of complex numbers ( de-moivre's theorem) in finding out the integral of type ∫sinmxcosnxdx , where both m,n are positive integers. ...

∫ x.tan x . dx ...

± ...

\hspace{-16}\bf{(1)\;\;\int \left(\frac{x^2-1}{x^2+1}\right).\frac{1}{\sqrt{x^4+1}}dx}$\\\\\\ $\bf{(2)\;\;\int \left(\frac{x^2+1}{x^2-1}\right).\frac{1}{\sqrt{x^4+1}}dx}$\\\\\\ $\bf{(3)\;\;\int \frac{\sqrt{x^4+1}}{x^4-1}dx}$\ ...

lim:t→x ( sinx-sint/x-t ) = f (sinx) Find range of f(x) (A) (-∞,1] (B) [-1,0] (C) [0,1] (D) [-1,∞) ...

∫ ln(x-1)/x ? ...

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A balloon in the form of a right circular cone is surmounted by a hemisphere, having a diameter equal to the height of the cone., is being inflated. how fast is its volume changing with respect to its total height h, when h=9 ...

What is the condition that the equation ax2+bx+c has a root in [0, 1]? In class, we integrated the given expression and arrived at the condition a/3 + b/2 +c=0. However, if we take the equation (x-2)(x-0.5)=0 ie x2- 5/2 x+1=0 ...

\hspace{-16}$(i) $\bf{\int\frac{1}{1+\sin^4 x}dx}$\\\\\\ (ii) $\bf{\int\frac{1}{1+\cos^4 x}dx}$ ...

Please use the shortest method possible and show the working ∫ 2 sin x + 3cosx/3sin x+4 cos x ...

Let f:R-->R be a continuous function such that f(x)-2f( x/2 )+f( x/4 ) = x2. f(3) is equal to (A) f(0) (B) 4+f(0) (C) 9+f(0) (D) 16+f(0). The equation f(x)-x-f(0) = 0 has exactly (A) No solution (B) One solution (C) Two so ...

\hspace{-16}\bf{\int_{0}^{1}x^{2013}.(1-x)^{2014}dx} ...

\hspace{-16}$How can I calculate Cont. and Diff. of $\bf{f(x) = \lim_{n\rightarrow \infty}\bold{\sqrt[2n]{\bold{\sin^{2n}x+\cos^{2n}x}}}}$ ...

Equation of the line through the point ( 1/2 ,2) and tangent to the parabola y = - x2/2 + 2 and secant to the curve y = 4 - x2 is (A) 2x + 2y - 5 = 0 (B) 2x + 2y - 3 = 0 (C) y-2 = 0 (D) None of these ...

Two curves C1 : y = x2 - 3 and C2 : y = kx2, k ε R intersect each other at two different points. The tangent drawn to C2 at one of the points of intersection A(a,y1), (a>0) meets C1 again at B (1, y2) (y1 ≠y2). The valu ...

Advanced 2 Q . 57 part (p) lim(x→0) √(2-2cosx)/2x = ? ...

Given:- k = lim (x→ ∞) [ Σ(k=1 to k=1000){ x + k} m ] / [ x m + 10 1000 ] where m > 101. ...

Among various properties of continuous, we have ƒ is continuous function on [a,b] and ƒ(a)ƒ(b) < 0, then there exists a point c in (a,b) such that ƒ(x) = 0 equivalently if ƒ is continuous on [a,b] and x ε R is such t ...

lim (x-> 0) [f(x)+log {1-(1/ef (x))}-log (f(x))]=0. Find f (0). ...

We are told that the height h, in metres, of a certain projectile as a function of time t, in seconds, is h = 20t*4.9t 2 .Find the domain and range for the function h(t). ...

\hspace{-16}$Calculate total no. of real solution in each case\\\\\\ $\bf{(1)\;\;2^x = 1+x^2}$\\\\\\ $\bf{(2)\;\; 2^x+3^x+4^x = x^2}$\\\\\\ $\bf{(3)\;\; 3^x+4^x+5^x = 1+x^2}$ ...

Lim X→0 ex-e sinx/ x-sinx Don't use L'Hospital ...

\hspace{-16}$Calculate total no. of real solution in $\bf{e ^x = x^n}$\\\\ where $\bf{n\in \mathbb{N}}$ ...

\hspace{-16}$Calculate total no. of real solution in each case\\\\\\ $\bf{(1)\;\;2^x = 1+x^2}$\\\\\\ $\bf{(2)\;\; 2^x+3^x+4^x = x^2}$\\\\\\ $\bf{(3)\;\; 3^x+4^x+5^x = 1+x^2}$ ...