Solve question

Solve question no:1of Exercise-6.8,you can use the highlighted theorems from the given attachment.This question is based on uniform continuity which comes under connectedness,completeness and compactness of Metric spaces.Attachment 1Attachment 2pi(x,y) <pi(x,a) +pi(a, b) +p,(b,y) <From (3) we then have [since f (x) = F(x) and f (y)= F(y)]33= 81.P2[ F(x), F(y)]<3.We conclude from (4), (5), and (6) thatMogot zredmana Lum Me ToP2 [ F(a), F(b) ]<eprovided only that p, (a, b) <8/3. This shows that F is uniformly continuous on Mi, andthe proof is complete.From 6.8F we see that neither f nor g in 6.8E is uniformly continuous.Exercises 6.81. Given E > 0 find 8 >0 such that[sin x – sina| <e(I.x – a| <8; – 00 <a < co ).[ Hint: Apply the theorem (or law) of the mean to f (x) =sinx.] Deduce that the sinefunction is uniformly continuous on ( – 00, co ).

“Struggling with a similar assignment?” We can help!!

How it works – it’s easy

Y

Place your Order

Submit your requirements through our small easy order form. Be sure to include and attach any relevant materials.

Make a payment

The total price of your order is based on number of pages, academic level and deadline.

i

Writing process

We assign the assignment to the most qualified tutor. When the tutor completes the assignment, it is transferred to one of our professional editors to make sure that the assignment meets all of your requirements.

Once complete, we’ll send your assignment via the email provided on the order form.

 

 

Achieve academic succes with the best online tutors.