021.11s.midterm

021.11s.midterm - ´(b Determine all(vertical and...

Info icon This preview shows pages 1–6. Sign up to view the full content.

View Full Document Right Arrow Icon
HKUST MATH021 Concise Calculus Midterm Examination Name: 6 Apr 2011 Student I.D.: 12:30–13:20 Signature: Directions: Do NOT open the exam until instructed to do so. All mobile phones and pagers should be switched OFF during the examination. You must show the steps in order to receive full credits. Electronic calculators are NOT allowed. This is a closed book examination. Answer ALL questions. Some formula: sin( x + y ) = sin x cos y + cos x sin y sin( x - y ) = sin x cos y - cos x sin y cos( x + y ) = cos x cos y - sin x sin y cos( x - y ) = cos x cos y + sin x sin y tan( x + y ) = tan x +tan y 1 tan x tan y sin 2 x = 2 sin x cos x cos 2 x = cos 2 x - sin 2 x = 2 cos 2 x - 1 = 1 - 2 sin 2 x sec 2 x = tan 2 x + 1 Question No. Points Out of 1 6 2 8 3 6 4 10 Total 30 1
Image of page 1

Info icon This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Answer all questions. Show all your work for full credit. 1. Compute the following limits. (a) lim θ →∞ sin 2 πθ θ = . (b) lim x 0 + x x = . 2
Image of page 2
2. Let f ( x ) = e x + 1. (a) The range of f is . (b) Given f is one-to-one on its domain. Compute the inverse of f . (c) The anti-derivative of f is . 3. Compute the derivative of f ( x ) = - x 2 using the definition of differentiation . 3
Image of page 3

Info icon This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Image of page 4
Image of page 5

Info icon This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Image of page 6
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: ´ (b) Determine all (vertical and horizontal) asymptote(s) of f ( x ). (c) Find f ′ ( x ) and f ′′ ( x ). f ′ ( x ) = ± ² ³ ´ and f ′′ ( x ) = ± ² ³ ´ . (d) Write down all critical point(s) of f ( x ): ± ² ³ ´ . (e) Find the interval(s) on which f is increasing and also the interval(s) on which f is decreasing. f ( x ) is increasing on the interval(s) ± ² ³ ´ and f ( x ) is decreasing on the interval(s) ± ² ³ ´ . 4 (f) Find the interval(s) on which f is concave up and also the interval(s) on which f is concave down. f ( x ) is concave up on the interval(s) ± ² ³ ´ and f ( x ) is concave down on the interval(s) ± ² ³ ´ . (g) Write down all inflection point(s) of f ( x ): ± ² ³ ´ . (h) Write down all root(s) of f (all x such that f ( x ) = 0): ± ² ³ ´ (i) Sketch f ( x ). 5- This page intentionally left blank for scratch work -6...
View Full Document

{[ snackBarMessage ]}

What students are saying

  • Left Quote Icon

    As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

    Student Picture

    Kiran Temple University Fox School of Business ‘17, Course Hero Intern

  • Left Quote Icon

    I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

    Student Picture

    Dana University of Pennsylvania ‘17, Course Hero Intern

  • Left Quote Icon

    The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

    Student Picture

    Jill Tulane University ‘16, Course Hero Intern