Transcribed TextTranscribed Text

1. Find the derivative of the following functions: *=1/142 y = 1 y=arctan Itz 1 2. Prove that the function f(x) = 0. is differentiable at I = 0 and find f'(0). 3. Suppose that f is continuous at I = 0. Prove that g(z) = xf(x) is differentiable at 0. 4. Suppose that the function f is defined on a, b] and that it is both left differentiable and right differentiable at CE (a,b). Prove that f is continuous at I = C. 5. Suppose that f and g are defined on R and that f is differentiable at I = q, but g is not. Prove or disprove: f + g is not differentiable at I = q. 6. Let f be a function defined on R and suppose there exists M > 0 such that, for any I. y R, If(x) - f(y)| < M/I - Prove that f is a constant function. 7. Suppose that f is differentiable at I = q, and let n € N. Find the limit I 8. Find the derivative of f(x) = log, 2.

Solution PreviewSolution Preview

These solutions may offer step-by-step problem-solving explanations or good writing examples that include modern styles of formatting and construction of bibliographies out of text citations and references. Students may use these solutions for personal skill-building and practice. Unethical use is strictly forbidden.

    By purchasing this solution you'll be able to access the following files:

    for this solution

    or FREE if you
    register a new account!

    PayPal, G Pay, ApplePay, Amazon Pay, and all major credit cards accepted.

    Find A Tutor

    View available Advanced Math Tutors

    Get College Homework Help.

    Are you sure you don't want to upload any files?

    Fast tutor response requires as much info as possible.

    Upload a file
    Continue without uploading

    We couldn't find that subject.
    Please select the best match from the list below.

    We'll send you an email right away. If it's not in your inbox, check your spam folder.

    • 1
    • 2
    • 3
    Live Chats