Question

The value of lim x—0 (16+5x)^1/4 -2 /(32+3x)^1/5 -2 is

Answer 1

Step-by-step explanation:

lim x—0 (16+5x)^1/4 -2 /(32+3x)^1/5 -2

use D-L hospitalization rule : Lim f'(x)/g'(x)

this rule apply for only 0/0 forms .

Lim (1/4)*(16+5x)^3/4 *(5) / (1/5)*(32+3x)^4/5 *(3) .....eq.(1)

in our question limit x--> 0 then

x = 0

apply in the equation 1

Lim (1/4)*(16+5x)^-3/4 *(5) / (1/5)*(32+3x)^-4/5 *(3)

= (1/4)(16)(5) / (1/5)(8)(3)

= (20)/(24)/5

= 100/24

= 50/12

= 25/6