मराठी
महाराष्ट्र राज्य शिक्षण मंडळएचएससी विज्ञान (सामान्य) इयत्ता १२ वी

Show that function f(x) = tan x is increasing in π(0,π2).

Advertisements
Advertisements

प्रश्न

Show that function f(x) = tan x is increasing in `(0, π/2)`.

बेरीज
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).

shaalaa.com
  या प्रश्नात किंवा उत्तरात काही त्रुटी आहे का?
2021-2022 (March) Set 1

व्हिडिओ ट्यूटोरियलVIEW ALL [3]

संबंधित प्रश्‍न

Test whether the function is increasing or decreasing. 

f(x) = `"x" -1/"x"`, x ∈ R, x ≠ 0, 


Show that the function given by f(x) = 3x + 17 is strictly increasing on R.


Show that y = `log(1+x) - (2x)/(2+x), x> -  1`, is an increasing function of x throughout its domain.


Water is dripping out from a conical funnel of semi-verticle angle `pi/4` at the uniform rate of `2 cm^2/sec`in the surface, through a tiny hole at the vertex of the bottom. When the slant height of the water level is 4 cm, find the rate of decrease of the slant height of the water.


Prove that the function f(x) = loga x is increasing on (0, ∞) if a > 1 and decreasing on (0, ∞), if 0 < a < 1 ?


Without using the derivative show that the function f (x) = 7x − 3 is strictly increasing function on R ?


Find the interval in which the following function are increasing or decreasing  f(x) = 6 − 9x − x2  ?


Find the interval in which the following function are increasing or decreasing f(x) = 8 + 36x + 3x2 − 2x?


Find the interval in which the following function are increasing or decreasing  f(x) = 5x3 − 15x2 − 120x + 3 ?


Find the interval in which the following function are increasing or decreasing \[f\left( x \right) = \frac{x^4}{4} + \frac{2}{3} x^3 - \frac{5}{2} x^2 - 6x + 7\] ?


Find the interval in which the following function are increasing or decreasing \[f\left( x \right) = 3 x^4 - 4 x^3 - 12 x^2 + 5\] ?


Find the interval in which the following function are increasing or decreasing \[f\left( x \right) = \frac{3}{2} x^4 - 4 x^3 - 45 x^2 + 51\] ?


Show that f(x) = e1/x, x ≠ 0 is a decreasing function for all x ≠ 0 ?


Find the intervals in which f(x) = log (1 + x) −\[\frac{x}{1 + x}\] is increasing or decreasing ?


Prove that the following function is increasing on R f \[(x) =\]3 \[x^5\] + 40 \[x^3\] + 240\[x\] ?


Find the set of values of 'b' for which f(x) = b (x + cos x) + 4 is decreasing on R ?


Write the interval in which f(x) = sin x + cos x, x ∈ [0, π/2] is increasing ?


Write the set of values of a for which f(x) = cos x + a2 x + b is strictly increasing on R ?


The function f(x) = xx decreases on the interval


The function f(x) = x2 e−x is monotonic increasing when


In the interval (1, 2), function f(x) = 2 | x − 1 | + 3 | x − 2 | is


Function f(x) = ax is increasing on R, if


The radius r of a right circular cylinder is increasing uniformly at the rate of 0·3 cm/s and its height h is decreasing at the rate of 0·4 cm/s. When r = 3·5 cm and h = 7 cm, find the rate of change of the curved surface area of the cylinder. \[\left[ \text{ Use } \pi = \frac{22}{7} \right]\]


The price P for demand D is given as P = 183 + 120 D – 3D2.
Find D for which the price is increasing.


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.


If the demand function is D = 50 - 3p - p2, find the elasticity of demand at (a) p = 5 (b) p = 2 ,  Interpret your result. 


Find the values of x for which the following functions are strictly increasing : f(x) = 2x3 – 3x2 – 12x + 6


Show that f(x) = x – cos x is increasing for all x.


For manufacturing x units, labour cost is 150 – 54x and processing cost is x2. Price of each unit is p = 10800 – 4x2. Find the values of x for which Revenue is increasing.


Show that function f(x) =`("x - 2")/("x + 1")`, x ≠ -1 is increasing.


Show that function f(x) =`3/"x" + 10`, x ≠ 0 is decreasing.


The slope of tangent at any point (a, b) is also called as ______.


The total cost function for production of articles is given as C = 100 + 600x – 3x2, then the values of x for which the total cost is decreasing is  ______


Show that the function f(x) = `(x - 2)/(x + 1)`, x ≠ – 1 is increasing


The sides of a square are increasing at the rate of 0.2 cm/sec. When the side is 25cm long, its area is increasing at the rate of ______


The function f(x) = 4 sin3x – 6 sin2x + 12 sinx + 100 is strictly ______.


Which of the following functions is decreasing on `(0, pi/2)`?


Let f be a real valued function defined on (0, 1) ∪ (2, 4) such that f '(x) = 0 for every x, then ____________.


The function f (x) = 2 – 3 x is ____________.


The function f(x) = `(4x^3 - 3x^2)/6 - 2sinx + (2x - 1)cosx` ______.


Let 'a' be a real number such that the function f(x) = ax2 + 6x – 15, x ∈ R is increasing in `(-∞, 3/4)` and decreasing in `(3/4, ∞)`. Then the function g(x) = ax2 – 6x + 15, x∈R has a ______.


Let f(x) = tan–1`phi`(x), where `phi`(x) is monotonically increasing for `0 < x < π/2`. Then f(x) is ______.


Let f : R `rightarrow` R be a positive increasing function with `lim_(x rightarrow ∞) (f(3x))/(f(x))` = 1 then `lim_(x rightarrow ∞) (f(2x))/(f(x))` = ______.


Find the values of x for which the function f(x) = `x/(x^2 + 1)` is strictly decreasing.


Which statement about \[f'(x)=0\] and constant behaviour is correct?


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×