Question

evaluate limit -> (5x cos x- 3 sin x)/ 2 x^2 + tan 2x

Answer 1

Lim(x→0) {5xcosx. - 3sinx }/(2x² + tan2x }

put x = 0 for checking which form of limit possible here,
x = 0 , then, 0/0 hence,
we can use L- Hospital rule .

Lim(x→0) { 5xcosx - 3(sinx/x)× x }/{ 2x² + (tan2x/2x) × 2x }

use ,
Lim(x→0) sinx/x = 1
Lim (x→0) tanx/x = 1

now,

Lim(x→0) { 5x. cosx - 3x }/{2x² + 2x }

Lim(x→0) { 5cosx - 3}/{2x + 2 }

now ,again put x = 0
we get fintie value
e.g { 5 × 1 - 3 }/{ 0 + 2}

= 2/2 = 1

hence, value of limit = 1

Answer 2

The ans of this ques is 1