If f(x)=2x+cot^(-1)x+log(sqrt(1+x^2)-x) ...

If `f(x)=2x+cot^(-1)x+log(sqrt(1+x^2)-x)` then `f(x)` (a)increase in `(0,oo)` (b)decrease in `[0,oo]` (c)neither increases nor decreases in `[0,oo]` (d)increase in `(-oo,oo)`

Topper's Solved these Questions

3D COORDINATION SYSTEM
CENGAGE PUBLICATION|Exercise DPP 3.1|11 Videos
APPLICATION OF INTEGRALS
CENGAGE PUBLICATION|Exercise All Questions|143 Videos

Similar Questions

Explore conceptually related problems

Let f(x)=xsqrt(4a x-x^2),(a >0)dot Then f(x) is (a). increasing in (0,3a) decreasing in (3a, 4a) (b). increasing in (a, 4a) decreasing in (5a ,oo) (c). increasing in (0,4a) (d). none of these

The function defined by f(x)=(x+2)e^(-x) is (a)decreasing for all x (b)decreasing in (-oo,-1) and increasing in (-1,oo) (c)increasing for all x (d)decreasing in (-1,oo) and increasing in (-oo,-1)

Show that the function given by f (x) = sin x is (a) increasing in (0,(pi)/(2)) (b) decreasing in ((pi)/(2) ,pi) (c) neither increasing nor decreasing in (0, pi )

For each of the following graphs, comment whether f(x) is increasing or decreasing or neither increasing nor decreasing at x = a.

Prove that the function given by f(x) = cos x is (a) decreasing in (0, pi ) (b) increasing in (pi, 2pi) , and (c) neither increasing nor decreasing in (0, 2pi) .

Let f be the function f(x)=cosx-(1-(x^2)/2)dot Then (a) f(x) is an increasing function in (0,oo) (b) f(x) is a decreasing function in (-oo,oo) (c) f(x) is an increasing function in (-oo,oo) (d) f(x) is a decreasing function in (-oo,0)

Let f(x)=x^4-4x^3+6x^2-4x+1. Then, (a) f increase on [1,oo] (b) f decreases on [1,oo] (c) f has a minimum at x=1 (d) f has neither maximum nor minimum

int_(0)^(oo)(dx)/([x+sqrt(1+x^(2))]^(n)

Let f:[-oo,0)->(1,oo) be defined as f(x)=(1+sqrt(-x))-(sqrt(-x)-x) then f(x) is (A) injective but not surjective (B) injective as well as surjective (C) neither injective nor surjective (D) surjective nut not injective

(i) The function f(x)=x^(3) is decreasing in (-oo, oo) (ii) The function f(x)=x^(4) is increasing in (-oo, 0) , then-

CENGAGE PUBLICATION-APPLICATION OF DERIVATIVES-All Questions

The function x^x decreases in the interval (a) (0,e) (b) (0,1) (c) (...
Text Solution
|
Let f(x)=|x^2-3x-4|,-1lt=xlt=4 Then a) f(x) is monotonically increasin...
Text Solution
|
If f(x)=2x+cot^(-1)x+log(sqrt(1+x^2)-x) then f(x) (a)increase in (...
Text Solution
|
Let x and y be two real variable such that x >0 and x y=1 . Find the m...
Text Solution
|
A box, constructed from a rectangular metal sheet, is 21 cm by 16cm by...
Text Solution
|
A wire of length a is cut into two parts which are bent, respectively,...
Text Solution
|
The maximum area of the rectangle whose sides pass through the vertice...
Text Solution
|
The vertices of a triangle are (0,0), (x ,cosx), and (sin^3x ,0),w h ...
Text Solution
|
Assertion Let f:R→R,f(x)=x^3+x^2+3x+sinx f(x) is one-one. Reason f(x) ...
Text Solution
|
The base of prism is equilateral triangle. The distance from the centr...
Text Solution
|
Let f(x)=2x-sinx and g(x)=3sqrtx . Then
Text Solution
|
Let f(x)=x^4-4x^3+6x^2-4x+1. Then, (a) f increase on [1,oo] (b) f dec...
Text Solution
|
The set of all x for which log(1+ x) le x is equal to …… .
Text Solution
|
The maximum value of the function f(x)=2x^3-15 x^2+36 x-48 on the set ...
Text Solution
|
Let f(x)={x e^(a x),x lt=0;x+a x^2-x^3,x >0 where a is a positive con...
Text Solution
|
Suppose f(x) is a function satisfying the following conditions : ...
Text Solution
|
It is given that equation 4x^3-3x-p=0 has a unique root in the interva...
Text Solution
|
Using the relation 2(1−cosx)<x^2 ,x=0 or prove that sin(tanx)≥x,∀ϵ[0,...
Text Solution
|
If P(1)=0a n d(d P(x))/(dx)gtP(x), for all xge1. Prove that P(x)>0...
Text Solution
|
If p(x) is a polynomial of degree 3 satisfying p(-1)=10 , p(1) =-6 a...
Text Solution
|