What is the limit when t approaches 0 of tan8t?/tan5t

Question

What is the limit when t approaches 0 of tan8t?/tan5t

1 Answer

Impact of this question

3051 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2017-02-21T08:11:26

$L t (t \to 0) \frac{tan 8 t}{tan 5 t} = \frac{8}{5}$ $Lt(t->0)(tan8t)/(tan5t)=8/5$

Explanation:

Let us first find $L t_{x \to 0} \frac{tan x}{x}$ $Lt_(x->0)tanx/x$

$L t_{x \to 0} \frac{tan x}{x} = L t_{x \to 0} \frac{sin x}{x cos x}$ $Lt_(x->0)tanx/x=Lt_(x->0)(sinx)/(xcosx)$

= $L t_{x \to 0} \frac{sin x}{x} \times L t_{x \to 0} \frac{1}{cos x}$ $Lt_(x->0)(sinx)/x xx Lt_(x->0)1/cosx$

= $1 \times 1 = 1$ $1xx1=1$

Hence $L t_{t \to 0} \frac{tan 8 t}{tan 5 t}$ $Lt_(t->0)(tan8t)/(tan5t)$

= $L t_{t \to 0} \frac{\frac{tan 8 t}{8 t}}{\frac{tan 5 t}{5 t}} \times \frac{8 t}{5 t}$ $Lt_(t->0)((tan8t)/(8t))/((tan5t)/(5t))xx(8t)/(5t)$

= $\frac{L t_{8 t \to 0} (\frac{tan 8 t}{8 t})}{L t_{5 t \to 0} (\frac{tan 5 t}{5 t})} \times \frac{8}{5}$ $(Lt_(8t->0)((tan8t)/(8t)))/(Lt_(5t->0)((tan5t)/(5t)))xx8/5$

= $\frac{1}{1} \times \frac{8}{5} = \frac{8}{5}$ $1/1xx8/5=8/5$

Science

Math

Humanities

... and beyond

What is the limit when t approaches 0 of tan8t?/tan5t

1 Answer

Explanation:

Related questions

Impact of this question