Question

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

Answer 1

`Lt(t->0)(tan8t)/(tan5t)=8/5`

Explanation:

Let us first find `Lt_(x->0)tanx/x`

`Lt_(x->0)tanx/x=Lt_(x->0)(sinx)/(xcosx)`

= `Lt_(x->0)(sinx)/x xx Lt_(x->0)1/cosx`

= `1xx1=1`

Hence `Lt_(t->0)(tan8t)/(tan5t)`

= `Lt_(t->0)((tan8t)/(8t))/((tan5t)/(5t))xx(8t)/(5t)`

= `(Lt_(8t->0)((tan8t)/(8t)))/(Lt_(5t->0)((tan5t)/(5t)))xx8/5`

= `1/1xx8/5=8/5`