Limits Of Trigonometric Functions

The correct answer is (C) : $%5Cfrac%7B-11%7D%7B9%7D$

$%5Clim_%7B%7Bx%20%5Cto%200%7D%7D%20%5Climits$ $%5Cfrac%7Bcos(sinx)%20-%20cosx%7D%7Bx%5E4%7D$ = $%5Clim_%7B%7Bx%20%5Cto%200%7D%7D%20%5Climits$ $%5Cfrac%7B2sin(x%20%2B%20sinx).sin(%5Cfrac%7Bx%20-%20sinx%7D%7B2%7D)%7D%7Bx%5E4%7D$
= $%5Clim_%7B%7Bx%20%5Cto%200%7D%7D%20%5Climits$ $2.%5Cfrac%7B(%5Cfrac%7B(%20x%20%2B%20sinx%20%7D%7B2%7D)(%5Cfrac%7Bx-sinx%7D%7B2%7D)%7D%7Bx%5E4%7D$
= $%5Clim_%7B%7Bx%20%5Cto%200%7D%7D%20%5Climits$ $%5Cfrac%7B1%7D%7B2%7D.$ $(%5Cfrac%7B(x%2Bx%20-%5Cfrac%7Bx%5E3%7D%7B3!%7D%2B%5Cfrac%7Bx%5E5%7D%7B5!%7D....)(x-x%2B%5Cfrac%7Bx%5E3%7D%7B3!%7D....%7D%7Bx%5E4%7D)$
= $%5Clim_%7B%7Bx%20%5Cto%200%7D%7D%20%5Climits$ $%5Cfrac%7B1%7D%7B2%7D.$ $(2-%5Cfrac%7Bx%5E2%7D%7B3!%7D%2B%5Cfrac%7Bx%5E4%7D%7B5!%7D....)(%5Cfrac%7B1%7D%7B3!%7D-%5Cfrac%7Bx%5E2%7D%7B5!%7D-1)$
= $%5Cfrac%7B1%7D%7B6%7D$

The correct answer is 1
Let,

x%20%2B%202cosx%20%3D%20a

x%20%2B%202%20%3D%20b

as%20%5Cspace%20x%20%E2%86%92%200%2C%20a%20%E2%86%92%202%20%5Cspace%20and%20%5Cspace%20b%20%E2%86%92%202

%5Cbegin%7Barray%7D%7Bl%7D%5Cdisplaystyle%20%5Clim_%7B%20x%5Cto%200%7D%5Cleft(%5Cfrac%7Ba%5E3%2B2a%5E2%2B3%5Csin%20a%7D%7Bb%5E3%20%2B%202b%5E2%20%2B%203%5Csin%20b%7D%5Cright)%5E%7B%5Cfrac%7B100%7D%7Bx%7D%7D%20%5Cend%7Barray%7D

%5Cbegin%7Barray%7D%7Bl%7D%3De%5E%7B%5Cdisplaystyle%20%5Clim_%7Bx%20%5Cto%200%7D%5Cfrac%7B100%7D%7Bx%7D.%5Cfrac%7B(a%5E3-b%5E3)%2B2(a%5E2-b%5E2)%2B3(%5Csin%20a%20%E2%80%93%20%5Csin%20b)%7D%7Bb%5E3%2B2b%5E2%20%2B%203%5Csin%20b%7D%7D%5Cend%7Barray%7D

%5Cbegin%7Barray%7D%7Bl%7D%5Cbecause%20%5Cdisplaystyle%20%5Clim_%7Bx%5Cto%200%7D%5Cfrac%7Ba-b%7D%7Bx%7D%3D%5Cdisplaystyle%20%5Clim_%7Bx%5Cto%200%7D%5Cfrac%7B2(%5Ccos%20x%20-1)%7D%7Bx%7D%3D0%5Cend%7Barray%7D

%3D%20e%5E0

%3D%201

High-Yield Trend

Chapter Questions
2 MCQs

Official Solution

Official Solution

Limits Of Trigonometric Functions

High-Yield Trend

Chapter Questions 2 MCQs

Official Solution

Official Solution

Chapter Questions
2 MCQs