Chapter Chosen

વિકલન

Book Chosen

ગણિત ધોરણ 11 સેમિસ્ટર 2

Subject Chosen

ગણિત

Book Store

Download books and chapters from book store.
Currently only available for
CBSE Gujarat Board Haryana Board

Previous Year Papers

Download the PDF Question Papers Free for off line practice and view the Solutions online.
Currently only available for
Class 10 Class 12

વ્યાખ્યાની મદદથી નીચેના વિધેયના આપેલ બિંદુએ વિકલિત શોધો :

2x + 3 ; x = 2 આગળ


અહીં, f (x) = 2x + 3

હવે, x = 2  આગળ f નો વિકલિત,

f apostrophe space open parentheses 2 close parentheses space equals space stack l i m with h rightwards arrow 0 below space space fraction numerator f space open parentheses 2 space plus space h close parentheses space minus space f space open parentheses 2 close parentheses over denominator h end fraction


space space space space space space space space space space space equals space stack l i m with h rightwards arrow 0 below space space fraction numerator 2 space open parentheses 2 space plus space h close parentheses space plus space 3 space minus space open parentheses 2 space open parentheses 2 close parentheses space plus space 3 close parentheses over denominator h end fraction


space space space space space space space space space space space equals space space stack l i m with h rightwards arrow 0 below space fraction numerator 4 space plus space 2 h space plus space 3 space minus space 7 over denominator h end fraction space equals space space 2 space equals space bold 2


વ્યાખ્યાની મદદથી નીચેના વિધેયના આપેલ બિંદુએ વિકલિત શોધો :
sin x ; x = 0  આગળ


અહીં, f (x) = sin x

હવે, x = 0 આગળ f નો વિકલિત,

straight f apostrophe space open parentheses 0 close parentheses space equals space limit as straight h rightwards arrow 0 of space space fraction numerator straight f space open parentheses 0 space plus space straight h close parentheses space minus space straight f space open parentheses 0 close parentheses over denominator straight h end fraction


        equals space limit as straight h rightwards arrow 0 of space space fraction numerator straight f space open parentheses straight h close parentheses space minus space straight f space open parentheses 0 close parentheses over denominator straight h end fraction


equals space limit as straight h rightwards arrow 0 of space fraction numerator sin space straight h space minus space sin space 0 over denominator straight h end fraction


equals space limit as straight h rightwards arrow 0 of space fraction numerator sin space straight h space minus space 0 over denominator straight h end fraction


equals space limit as straight h rightwards arrow 0 of space space fraction numerator sin space straight h over denominator straight h end fraction space equals space bold 1


વ્યાખ્યાની મદદથી નીચેના વિધેયના આપેલ બિંદુએ વિકલિત શોધો :

fraction numerator 3 straight x space plus space 2 over denominator 2 straight x space plus space 3 end fraction space semicolon space x space equals space 1 આગળ


bold અહ ીં bold comma space straight f space left parenthesis straight x right parenthesis space equals space fraction numerator 3 straight x space plus space 2 over denominator 2 straight x space plus space 3 end fraction

bold હવ ે comma space straight x space equals space 1 space bold આગળ bold space bold f bold space bold ન ો bold space bold વ િ કલ િ ત bold comma

straight f apostrophe left parenthesis 1 right parenthesis space equals space limit as straight h rightwards arrow 0 of space space fraction numerator straight f space left parenthesis 1 space plus space straight h space right parenthesis space minus space straight f space left parenthesis 1 right parenthesis over denominator straight h end fraction


       equals space limit as straight h rightwards arrow 0 of space fraction numerator begin display style fraction numerator 3 open parentheses 1 space plus space straight h close parentheses space plus space 2 over denominator 2 space open parentheses 1 space plus space straight h close parentheses space plus space 3 end fraction end style space minus space begin display style fraction numerator 3 space left parenthesis 1 right parenthesis space plus space 2 over denominator 2 space left parenthesis 1 right parenthesis space plus space 3 end fraction end style over denominator straight h end fraction


equals space limit as straight h rightwards arrow 0 of space fraction numerator begin display style fraction numerator 5 space plus space 3 straight h over denominator 5 space plus space 2 straight h end fraction end style space minus space 1 over denominator straight h end fraction


equals space limit as straight h rightwards arrow 0 of space fraction numerator 5 space plus space 3 straight h space minus space 5 space minus space 2 straight h over denominator straight h space open parentheses 5 space plus space 2 straight h close parentheses end fraction


equals space limit as straight h rightwards arrow 0 of space space fraction numerator straight h over denominator straight h space open parentheses 5 space plus space 2 straight h close parentheses end fraction


equals space limit as straight h rightwards arrow 0 of space fraction numerator 1 over denominator 5 space plus space 2 straight h end fraction


equals space fraction numerator 1 over denominator 5 space plus space 0 end fraction


equals space bold 1 over bold 5

વ્યાખ્યાની મદદથી નીચેના વિધેયના આપેલ બિંદુએ વિકલિત શોધો :

3 straight x squared space minus space 2 straight x space plus space 1 space semicolon space straight x space equals space minus 1 spaceઆગળ


અહીં, straight f space left parenthesis straight x right parenthesis space equals space 3 straight x squared space minus space 2 straight x space plus space 1

હવે, x = -1 આગળ f નો વિકલિત,

straight f apostrophe space open parentheses negative 1 close parentheses space equals space limit as straight h rightwards arrow 0 of space space fraction numerator straight f space open parentheses negative 1 space plus space straight h close parentheses space minus space straight f space open parentheses negative 1 close parentheses over denominator straight h end fraction


           equals space limit as straight h rightwards arrow 0 of space space fraction numerator open parentheses 3 open parentheses negative 1 space plus space straight h close parentheses squared space minus space 2 space open parentheses negative 1 space plus space straight h close parentheses space plus space 1 close parentheses space minus space open parentheses 3 open parentheses negative 1 close parentheses squared space minus space 2 space open parentheses negative 1 close parentheses plus space 1 close parentheses over denominator straight h end fraction


equals space limit as straight h rightwards arrow 0 of space fraction numerator open parentheses 3 open parentheses 1 space minus space 2 straight h space plus space straight h squared space close parentheses space plus space 2 space minus space 2 straight h space plus space 1 close parentheses space minus space open parentheses 3 space plus space 2 space plus space 1 close parentheses over denominator straight h end fraction


equals space limit as straight h rightwards arrow 0 of space fraction numerator 3 space minus space 6 straight h space plus space 3 straight h squared space plus space 3 space minus space 2 straight h space minus space 6 over denominator straight h end fraction


equals space limit as straight h rightwards arrow 0 of space space fraction numerator 3 straight h squared space minus space 8 straight h over denominator straight h end fraction


equals space limit as straight h rightwards arrow 0 of space space open parentheses 3 straight h space minus space 8 close parentheses

equals space 0 space minus 8

equals space bold minus bold space bold 8


વ્યાખ્યાની મદદથી નીચેના વિધેયના આપેલ બિંદુએ વિકલિત શોધો :
1 over straight x space semicolon space x space equals space 1 આગળ


અહીં, f (x) = 1 over straight x

હવે, x = 1 આગળ f નો વિકલિત,

straight f apostrophe space open parentheses 1 close parentheses space equals space limit as straight h rightwards arrow 0 of space fraction numerator straight f space open parentheses 1 space plus space straight h close parentheses space minus space straight f space open parentheses 1 close parentheses over denominator straight h end fraction


        equals space limit as straight h rightwards arrow 0 of space space fraction numerator begin display style fraction numerator 1 over denominator 1 space plus space straight h end fraction end style space minus space begin display style 1 over 1 end style over denominator straight h end fraction


equals space limit as straight h rightwards arrow 0 of space fraction numerator 1 space minus space open parentheses 1 space plus space straight h close parentheses over denominator straight h space open parentheses 1 space plus space straight h close parentheses end fraction


equals space limit as straight h rightwards arrow 0 of space fraction numerator negative straight h over denominator straight h space open parentheses 1 space plus space 4 close parentheses end fraction

equals space limit as straight h rightwards arrow 0 of space space fraction numerator negative 1 over denominator 1 space plus space straight h end fraction


equals space fraction numerator negative 1 over denominator 1 space plus space 0 end fraction

equals space bold minus bold space bold 1