View the step-by-step solution to:

Question

Q1. Let f(x)=√x(1+sin(π/x)), x>0. Determine whether it is possible to extend f to a continuous function ˜ f

over[0,+∞).


Q2. Let g(x)=(x2+1)sinx.

(a) Without using differentiability of g, explain why g is continuous.

(b) Explain why g is differentiable, and then find the derivative of g.


Q3.Let f(x)=∣x+3∣3/2/ ∣x−4∣ .

(a) Write f as a case-defined function.

(b) Compute the derivative of f. You should determine when you can use the formulas of derivatives and rules of differentiation and when you should apply the definition of derivative.

Top Answer

View the full answer
limit behavior.jpg

Sign up to view the full answer

Why Join Course Hero?

Course Hero has all the homework and study help you need to succeed! We’ve got course-specific notes, study guides, and practice tests along with expert tutors.

-

Educational Resources
  • -

    Study Documents

    Find the best study resources around, tagged to your specific courses. Share your own to gain free Course Hero access.

    Browse Documents
  • -

    Question & Answers

    Get one-on-one homework help from our expert tutors—available online 24/7. Ask your own questions or browse existing Q&A threads. Satisfaction guaranteed!

    Ask a Question