e106fk

# e106fk - MAC 2311 Exam I and Key Prof S Hudson 1[25pt Short...

This preview shows pages 1–2. Sign up to view the full content.

MAC 2311 Sept 27, 2006 Exam I and Key Prof. S. Hudson 1) [25pt] Short answer problems: a) Solve for x , given that | x - 1 | < x + 1. b) Solve for x , given that cos(2 x ) = 0. c) Solve for x , given that log 10 (1 + x ) = 3. d) Complete the identity (no explanation required): sin(2 α ) = e) Complete the identity (calculate, using a triangle): sin(cos - 1 x ) = 2) [10pt] Find parametric equations for the portion of the parabola x = y 2 joining (1,-1) to (1,1), oriented upwards. 3) [15pts] Answer True or False. You do not have to explain. a) If f is continuous at 2, then lim x 2 + f ( x ) exists. b) If lim x 2 - f ( x ) exists, then lim x 2 + f ( x ) exists. c) If x is a number so that | x - 2 | < 1, then | x - 4 | < 5. d) > 0 , δ > 0 , δ + < . 001. e) A rational function is continuous at every point where the denominator is nonzero. 4) (25pt) Compute the following limits. Notice that 3 are one-sided. You may have to answer, for example, with ‘d.n.e.’ or ‘+ ’ [the latter will get more credit, if it is correct]. a) lim x 3 + x x 2 - 9 = b) lim x 1 + x 4 - 1 x - 1 = c) lim x →-∞ e x + e - x e x - e - x = d) lim x 0 - e 1 /x = e) lim x 0 x +4 - 2 x = 5) [10pt] Use the method of Ex 1 in Ch 2.1 (use a limit) to find the equation of the tangent

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

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

### What students are saying

• 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.

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

• 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.

Dana University of Pennsylvania ‘17, Course Hero Intern

• 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.

Jill Tulane University ‘16, Course Hero Intern