Advertisements
Advertisements
प्रश्न
Show that function f(x) = tan x is increasing in `(0, π/2)`.
Advertisements
उत्तर
Given, f(x) = tan x
f'(x) = sec2x
But sec2x > 0, ∀x∈ (0, π/2)
Hence f(x) = tan x is strictly increasing in (0, π/2).
APPEARS IN
संबंधित प्रश्न
Price P for demand D is given as P = 183 +120D - 3D2 Find D for which the price is increasing
Find the value(s) of x for which y = [x(x − 2)]2 is an increasing function.
The function f (x) = x3 – 3x2 + 3x – 100, x∈ R is _______.
(A) increasing
(B) decreasing
(C) increasing and decreasing
(D) neither increasing nor decreasing
The interval in which y = x2 e–x is increasing is ______.
Show that f(x) = \[\frac{1}{x}\] is a decreasing function on (0, ∞) ?
Find the interval in which the following function are increasing or decreasing f(x) = x2 + 2x − 5 ?
Find the interval in which the following function are increasing or decreasing f(x) = (x − 1) (x − 2)2 ?
Show that f(x) = cos x is a decreasing function on (0, π), increasing in (−π, 0) and neither increasing nor decreasing in (−π, π) ?
Find the intervals in which f(x) = log (1 + x) −\[\frac{x}{1 + x}\] is increasing or decreasing ?
Prove that the function f given by f(x) = log cos x is strictly increasing on (−π/2, 0) and strictly decreasing on (0, π/2) ?
Prove that the function f(x) = cos x is:
(i) strictly decreasing in (0, π)
(ii) strictly increasing in (π, 2π)
(iii) neither increasing nor decreasing in (0, 2π).
Write the set of values of 'a' for which f(x) = loga x is decreasing in its domain ?
Find 'a' for which f(x) = a (x + sin x) + a is increasing on R ?
State whether f(x) = tan x − x is increasing or decreasing its domain ?
The function f(x) = xx decreases on the interval
If the function f(x) = 2x2 − kx + 5 is increasing on [1, 2], then k lies in the interval
Let \[f\left( x \right) = \tan^{- 1} \left( g\left( x \right) \right),\],where g (x) is monotonically increasing for 0 < x < \[\frac{\pi}{2} .\] Then, f(x) is
Function f(x) = ax is increasing on R, if
If x = cos2 θ and y = cot θ then find `dy/dx at θ=pi/4`
The consumption expenditure Ec of a person with the income x. is given by Ec = 0.0006x2 + 0.003x. Find MPC, MPS, APC and APS when the income x = 200.
Find `dy/dx,if e^x+e^y=e^(x-y)`
If the demand function is D = 50 - 3p - p2, find the elasticity of demand at (a) p = 5 (b) p = 2 , Interpret your result.
The edge of a cube is decreasing at the rate of`( 0.6"cm")/sec`. Find the rate at which its volume is decreasing, when the edge of the cube is 2 cm.
Test whether the following functions are increasing or decreasing: f(x) = `x-(1)/x`, x ∈ R, x ≠ 0.
Find the values of x for which the following functions are strictly increasing : f(x) = 2x3 – 3x2 – 12x + 6
Find the values of x for which the function f(x) = x3 – 12x2 – 144x + 13 (a) increasing (b) decreasing
Show that f(x) = x – cos x is increasing for all x.
Solve the following : Find the intervals on which the function y = xx, (x > 0) is increasing and decreasing.
Find the value of x, such that f(x) is increasing function.
f(x) = 2x3 - 15x2 - 144x - 7
Prove that function f(x) = `x - 1/x`, x ∈ R and x ≠ 0 is increasing function
If the function f(x) = `7/x - 3`, x ∈ R, x ≠ 0 is a decreasing function, then x ∈ ______
The function f(x) = 9 - x5 - x7 is decreasing for
For every value of x, the function f(x) = `1/"a"^x`, a > 0 is ______.
For which interval the given function f(x) = 2x3 – 9x2 + 12x + 7 is increasing?
For every value of x, the function f(x) = `1/7^x` is ______
Let the f : R → R be defined by f (x) = 2x + cosx, then f : ______.
The values of a for which the function f(x) = sinx – ax + b increases on R are ______.
The function f(x) = tan-1 (sin x + cos x) is an increasing function in:
Which of the following graph represent the strictly increasing function.
Let x0 be a point in the domain of definition of a real valued function `f` and there exists an open interval I = (x0 – h, ro + h) containing x0. Then which of the following statement is/ are true for the above statement.
Let f(x) be a function such that; f'(x) = log1/3(log3(sinx + a)) (where a ∈ R). If f(x) is decreasing for all real values of x then the exhaustive solution set of a is ______.
Function f(x) = `log(1 + x) - (2x)/(2 + x)` is monotonically increasing when ______.
y = log x satisfies for x > 1, the inequality ______.
Read the following passage:
|
The use of electric vehicles will curb air pollution in the long run. V(t) = `1/5 t^3 - 5/2 t^2 + 25t - 2` where t represents the time and t = 1, 2, 3, ...... corresponds to years 2001, 2002, 2003, ...... respectively. |
Based on the above information, answer the following questions:
- Can the above function be used to estimate number of vehicles in the year 2000? Justify. (2)
- Prove that the function V(t) is an increasing function. (2)
Let f(x) = x3 – 6x2 + 9x + 18, then f(x) is strictly increasing in ______.
Find the values of x for which the function f(x) = `x/(x^2 + 1)` is strictly decreasing.
