Question

Check my answers. Limits

Answer 1

Typing the answers now.

Answer 2

(a)
\[\frac{ \frac{ sinx }{ cosx } }{ 4x } = \frac{ 1 }{ 4 } \times \frac{ sinx }{ x } \times \frac{ 1 }{ cosx } \]
= \[\frac{ 1 }{ 4 } \times 1 \times \frac{ 1 }{ 1 }=\frac{ 1 }{ 4 }\]

Answer 3

(b)
\[\lim_{x \rightarrow \infty}[\frac{ \sin(2\sin \frac{ 1 }{ x }) }{ 2\sin \frac{ 1 }{ x } }\times \frac{ \sin \frac{ 1 }{ x } }{ \frac{ 1 }{ x } } \times 2\]
= 1 * 1 * 2 = 2

Answer 4

Good. It's wise to remember that as x tends to infinity, both sinx/x and tan x/x becomes 1.

Answer 5

Okay Okay, thanks again x2 :)

Answer 6

Sorry x tends to zero.

Answer 7

Yw :)