यदि f(2) = 4 और f'(2)=1, तब `lim_(x to 2)(xf(2)-2f(x))/(x-2) ` का मान ज्ञात कीजिए ।

Explanation

चूँकि `f(2)=4 " " `…(1)
और `f'(2)=1`
`rArr lim_(x to 2) (f(x)-f(2))/(x-2)=1 " " `…(2)
` " " ` [अवकलनीयता की परिभाषा से]
अब `lim_(x to 2) (xf(2)-2f(x))/(x-2)`
`rArr lim_(x to2) (xf(2)-2f(2)+2f(2)-2f(x))/((x-2))`
`=lim_(x to 2) ((x-2)f(2)-2{f(x)-f(2)})/(x-2)`
`lim_(x to 2)[((x-2)f(2))/(x-2)-2{(f(x)-f(x))/(x-2)}]`
`=lim_(x to 2) f(2)-2xxlim_(x to 2) (f(x)-f(2))/(x-2)`
`=f(2)- 2xx f'(2)`
`=4-2xx1, " " ` [ समी (1 ) और (2 ) से]
`=4-2=2`.