Question

Find the following limits.
`(i)" "lim_(xto2) (4x)/(x^(3)-3)" "(ii)" "lim_(xto1)(log_(10)x-3)/(3x-2)" "(iii)" "lim_(xto pi) (3+cosx)/(2-sinx)`

Answer 1

In each of the given limits function is defined and contin-uously exists in the NBD of x where we have to find the limit. So, we will find the limits unsing the direct substitution
`(i)" "underset(xto2)lim(4x)/(x^(3)-3)=(4(2))/((2)^(3)-3)=8/5" "(ii)underset(xto1)lim(log_(10)x-3)/(3x-2)=((log_(10)1)-3)/(3(1)-2)=(0-3)/(1)=-3" "(iii)underset(xtopi)lim(3+cosx)/(2-sinx)=(3+cospi)/(2-sinpi)=(3-1)/(2-0)=1`