Question

`lim_(xrarr0) ((1-cos2x)(3+cosx))/(xtan4tanx)` is equal to
A. `-(1)//(4)`
B. `(1)//(2)`
C. `1`
D. `2`

Answer 1

Correct Answer - D
`lim_(xto0) ((1-cos2x)(3+cosx))/(xtan4tanx)`
` lim_(xto0) 2 ((sin^2x)/x)((3+cosx))/(((tan4x)/(4x))4x)`
` =lim_(xto0) (2)/(4) ((sinx)/(x))^2xx(1)/((tan4x)/(4x)))xx(3+cos x) `
`=(2)/(4)xx(1)^2xx(1)/(1)xx(3+1)=2`