Recently Active Calculus Questions

A tank contains 100 Litres of an aqueous solution containing 10 Kg of salt water is entering in the tank at the rate of 3 Litres per minute and the mixture is flowing out at 2 litre per minute, the concentric is maintained un ...

f(x)= (e[x]+|x| -2)/[x]+|x| Find limit of f(x) when x tends to 0.[x] stands for G.I.F and |x| denotes the modulus sign. ...

1,limit (x-:0) is abbreviated as L0 L0f(x) = l , which is real, then a) L0f(x2) = l2 b) L0f( x/l ) = 1 c) L0f(2x) = 2l d) L0f(-x) = l 2,If La f(x) and Lag(x) exist finitely then an incorrect statement among the following a) L ...

\hspace{-16}$For each Integer $\mathbf{n\geq 2}$.Determine the values of the integrals\\\\ $\mathbf{(1)\;\;I_{n,3}= \int \sin^3x.\sin (nx)dx}$\\\\ $\mathbf{(2)\;\;I_{n,5}= \int \sin^5x.\sin (nx)dx}$\\\\ ...

Q4 Let f(x) = ln(2x-x2) + sin Î x/2, then a) Graph of f is symmetrical about the line x=1 b) graph of f is symetrical about the line x=2 c) maximum value of f is 1 d) minimum value of f does not exist ...

Q1 If f(x) and g(x) be periodic and non periodic functions respectively, then f(g(x)) is a) always periodic b) never periodic c) periodic when g(x) is a linear function of x d) can't say Answer is c. Please tell why it is not ...

\hspace{-16}\mathbf{\int\frac{\sqrt{1-x^2}-x}{x^3-x^2-x+1-\sqrt{1-x^2}+x\sqrt{1-x^2}}dx} ...

Show that : *Image* ...

\hspace{-16}$If $\mathbf{x,y>0}$ and $\mathbf{f(x,y)=\sin^{-1}\left(\frac{x}{1+x^2}\right)+\sin^{-1}\left(\frac{y^2+y+1}{y^4+1}\right)}$\\\\\\ Then Find $\mathbf{\mathbb{R}}$ange of The Following $\mathbf{\mathbb{E}}$xpres ...

\hspace{-16}(1)\;\; \int\frac{x^3}{(1+x^3)^2}dx\\\\\\ (2)\;\; \int\frac{2012x-1}{e^{2012x}-2011x}dx ...

\hspace{-16}(1)\;\; \int\frac{\sin^{3n-1}.\cos^{n-1}}{\sin^{4n}x+\cos^{4n}x}dx$\\\\\\ Where $n\in\mathbb{N}$ ...

\hspace{-16}\mathbf{\int \sin (101\;x).\sin^{99}\;xdx} ...

\hspace{-16}$If each side of Square $\mathbf{OABC}$ is $\mathbf{4}\;$unit\\\\ and There are $\mathbf{4}$ Quarter Circle Center at Corrosponding Vertex\\\\ Then Find Area of Region denoted by $\mathbf{\bold{\alpha}}$ and $\mat ...

1)f(x) and g(x) are linear functions for all x such that f(g(x)) and g(f(x)) are Identity functions.If f(0)=4 and g(5)=17 find f(2006)? 2)let f(x)=(x+1)(x+2)(x+3)(x+4)+5 where x belongs to [-6,6].If range of f(x) is [a,b] whe ...

\hspace{-16}\mathbf{\int\frac{x.\sin^2 x}{\cos (2x).\cos^2 x}dx} ...

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

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

Evaluate: ∫01 xa-1/ln x dx ...

f(x)=ax3+bx2+cx+dsin x. Findthe condition that f(x) is always injective function. 2. Let f: X→Y be a function defined by f(x)= a sin(x+pi/4)+b cos x+c.If f(x) is bijective,find X. ...

\hspace{-16}$If $\mathbf{f:\mathbb{N}\rightarrow \mathbb{R}}$ be a function such that $\mathbf{f(1)=\frac{2007}{6}}$ and \\\\\\ $\mathbf{\frac{f(1)}{1}+\frac{f(2)}{2}+\frac{f(3)}{3}+.........+\frac{f(n)}{n}=\frac{n+1}{2}.f(n) ...

If the function f:R→A given by f(x)= ex-e-|x|/ex+e|x| is surjectoon then find A. ...

f\left(x \right)=\cos \left(\frac{\Pi }{x} \right) then prove that f(x) is increasing in the interval \left(\frac{1}{2n+1} ,\frac{1}{2n}\right) n\epsilon N ...

how to use latex? ...

Evaluate the following integral: ∫ √cos2x/sinx dx Plz show me the steps also. ...

Find range: f(x)= sin2x+sinx-1/sin2x-sinx+2 ...

For which of the following, y can be a function of x? 1. x4=y2 2.y=(log x)2 ...

1) Find the value of limit |x|[cosx] where x tends to 0.. [.] is the Greatest integer function.. 2) Find the value of limit (xy-yx)/(xx-yy) where x tends to y. 3) Find the solution of 2x+2|x|>= 2√2. Please provide the pr ...

Q1:f(x)=(-1)[x] is even or odd?[.] is GINT. Q2: If f:[-20,20]→R given by f(x)=[ x2/a ]sin x+cos x is an even function.then find a.[.] is GINT. ...

There are exactly two linear functions,which map[-1,1] onto [0,3].Then find the point of their intersection. ...

Determine whether the following function is even or odd f(x+y)+f(x-y)=2f(x)f(y). f(0)≠0.x,y are reals. ...