Home
Class 12
MATHS
For 0 < x lt=pi/2, show that x-(x^3)/6< ...

For `0 < x lt=pi/2, `show that `x-(x^3)/6< sin(x) < x dot`

Text Solution

AI Generated Solution

To prove the inequality \( x - \frac{x^3}{6} < \sin(x) < x \) for \( 0 < x \leq \frac{\pi}{2} \), we will break it down into two parts: 1. Show that \( \sin(x) < x \). 2. Show that \( x - \frac{x^3}{6} < \sin(x) \). ### Step 1: Proving \( \sin(x) < x \) Let \( f(x) = \sin(x) - x \). ...
Promotional Banner

Topper's Solved these Questions

  • MONOTONICITY AND MAXIMA MINIMA OF FUNCTIONS

    CENGAGE ENGLISH|Exercise Concept Application Exercise 6.3|5 Videos

  • MONOTONICITY AND MAXIMA MINIMA OF FUNCTIONS

    CENGAGE ENGLISH|Exercise Concept Application Exercise 6.4|17 Videos

  • MONOTONICITY AND MAXIMA MINIMA OF FUNCTIONS

    CENGAGE ENGLISH|Exercise Concept Application Exercise 6.1|10 Videos

  • METHODS OF DIFFERENTIATION

    CENGAGE ENGLISH|Exercise Single Correct Answer Type|46 Videos

  • MONOTONOCITY AND NAXINA-MINIMA OF FUNCTIONS

    CENGAGE ENGLISH|Exercise Comprehension Type|6 Videos

Similar Questions

Explore conceptually related problems

A study was conduced to find out the concentration of sulphur dioxide in the air in parts per million (ppm) of a certain city. The data obtained for 30 days is as follow: {:("0.03 0.08 0.08 0.09 0.04 0.17"),("0.16 0.05 0.02 0.06 0.18 0.20"),("0.11 0.08 0.12 0.13 0.22 0.07"),("0.08 0.01 0.10 0.06 0.09 0.18"),("0.11 0.07 0.05 0.07 0.01 0.04"):} You were asked to prepare a frequency distribution table, regarding the concentration of sulphur dioxide in the air in parts per million of a certain city for 30 days. Using this table, find the probability of the concentration of sulphur dioxide in the interval 0.12-0.16 on any of these days.

If A dn B be 3xx3 matrices the AB=0 implies (A) A=0 or B=0 (B) A=0 and B=0 (C) |A|=0 or |B|=0 (D) |A|=0 and |B|=0

Four identical charges are placed at the points (1,0,0), (0,1,0),(-1,0,0) , and (0,-1,0) . Then,

The vertices of a triangle are (0, 0), (1,0) and (0,1). Then excentre opposite to (0, 0) is

The value of 0. 23 +\ 0. 22 is (a) 0. 45 \ (b) 0. 43 \ (c) 0. 47 \ (d) 0. 41

A study was conducted to find out the concentration of sulphur dioxide in the air in parts per million (ppm) of a certain city. The data obtained for 30 days is as follows: 0.03 0.08 0.08 0.09 0.04 0.170.16 0.05 0.02 0.06 0.18 0.200.11 0.08 0.12 0.13 0.22 0.070.08 0.01 0.10 0.06 0.09 0.180.11 0.07 0.05 0.07 0.01 0.04 (i) Make a grouped frequency distribution table for this data with class intervals as 0.00 - 0.04, 0.04 - 0.08, and so on.(ii) For how many days, was the concentration of sulphur dioxide more than 0.11 parts per million?

If A=[(0,0,0,0),(0,0,0,0),(1,0,0,0),(0,1,0,0)] then (A) A^2=I (B) A^2=0 (C) A^3=0 (D) none of these

The inverse of the matrix [(0,0,1),(0,1,0),(1,0,0)] is (A) [(0,0,1),(0,1,0),(1,0,0)] (B) [(0,0,-1),(0,-1,0),(-1,0,0)] (C) [(1,0,0),(0,1,0),(0,0,1)] (D) [(1/2,0,0),(0,1/2,0),(0,0,1/2)]

Out of the following matrices, choose that matrix which is a scalar matrix: a) [(0 ,0),( 0, 0)] (b) [(0, 0, 0),( 0 ,0, 0)] (c) [(0, 0),( 0, 0),( 0 ,0)] (d) [(0),(0),( 0) ]

If P=[(x,0, 0),( 0,y,0 ),(0, 0,z)] and Q=[(a,0 ,0 ),(0,b,0 ),(0, 0,c)] , prove that P Q=[(x a,0 ,0 ),(0,y b,0),( 0 ,0,z c)]=Q P