V63_0121_0007_2008F_Midterm

V63_0121_0007_2008F_Midterm - f ( x ). (b) (5 points)...

Info iconThis preview shows pages 1–7. Sign up to view the full content.

View Full Document Right Arrow Icon
Name: Midterm Exam Calculus I 2:00 - 3:15 pm, October 15, 2008 This examination booklet contains 6 problems on 7 sheets of paper including the front cover. Do all of your work in this booklet and show all your computations. This is a closed book exam. No calculators are allowed. 1 2 3 4 5 6 Total
Background image of page 1

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

View Full DocumentRight Arrow Icon
1. Compute the following limits (6 points each). (a) lim x →− 3 x 2 - 9 x 2 + 2 x - 3 (b) lim x →∞ 5 x 4 - 2 x + 1 - 2 x 4 + 4 x 3 + 3 (c) lim x 0 x 2 tan 2 (2 x )
Background image of page 2
2. (15 points) Let f ( x ) = - x + 1 if x < 0 5 - x if 0 x < 3 ( x - 3) 2 + 2 if x > 3 (a) Compute the following limits lim x 0 f ( x ) , lim x 0+ f ( x ) , lim x 0 f ( x ) lim x 3 f ( x ) , lim x 3+ f ( x ) , lim x 3 f ( x ) (b) Where is the function discontinuous? Explain why.
Background image of page 3

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

View Full DocumentRight Arrow Icon
3. (a) (10 points) Let f ( x ) = x . Use the defnition oF derivative to compute
Background image of page 4
Background image of page 5

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

View Full DocumentRight Arrow Icon
Background image of page 6
Background image of page 7
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: f ( x ). (b) (5 points) Compute the equation oF the line tangent to f ( x ) at x = 4. 4. Calculate y ( x ) (7 points each): (a) y = 2( x-1) 3 + 5 x-1 (b) y = x 2 cos( x + 2) (c) y = x + 1 1-x (d) y = 1 sin( x-cos( x )) 5. (12 points) Use implicit diferentiation to calculate y ( x ): x tan(3 y ) = x 2 y + xy 2-1 6. (a) Use intermediate value theorem to show that f ( x ) = 2 x 3-4 x 2-5 x + 4 = 0 has a root in the interval [0 , 2]. (6 points) (b) Show that f ( x ) = 0 has another root. (6 points)...
View Full Document

This note was uploaded on 10/25/2010 for the course MATH V63.-0121- taught by Professor Staff during the Fall '08 term at NYU.

Page1 / 7

V63_0121_0007_2008F_Midterm - f ( x ). (b) (5 points)...

This preview shows document pages 1 - 7. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online