This preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Unformatted text preview: (c) [3 points] What is the total distance the object travels in the first three seconds? ( Hint : Figure out when it changes direction.) Page 2 Math 171: Exam 2 3. Evaluate the following limits, or explain why they do not exist. (a) [6 points] lim x → 2 x 2 √ 5 + x 2 3 . (b) [6 points] lim x → 3 1 x 2 3 x . (c) [6 points] lim x →∞ √ x 2 + 1 x + 1 Page 3 Math 171: Exam 2 4. [15 points] Sketch a graph of y = ( x 1) x 2 (2 x 1) 2 ( x + 1) . Find and label the horizontal and vertical asymptotes and all intercepts. Page 4 Math 171: Exam 2 5. Let f ( x ) = 1 2 x 1 . (a) [6 points] Express f ( x ) as a limit. (b) [6 points] Using the limit definition of the derivative, find f ( x ). Page 5 Math 171: Exam 2 6. Find the following derivatives. Do not simplify. (a) [7 points] Find d dx p x + (5 x 2 + 1) 100 . (b) [7 points] d dx (2 x + 1) √ x 3 x 2 + 1 . Page 6 Math 171: Exam 2 7. (a) [6 points] Give the definition of “ f ( x ) is continuous at x = c .” (b) [6 points] Explain why f ( x ) = x 3 x 2 5 √ x + 1 has a root in the interval [0 , 3]. Page 7 Math 171: Exam 2 8. (a) [6 points] Find the tangent line to the graph of x 2 y 2 2 = y at (1 , 2). (b) [6 points] If dy dx = x y 2 , find d 2 y dx 2 . Be sure to express your answer only in terms of x and y . Page 8...
View
Full Document
 Fall '07
 GOMEZ,JONES
 Math, Calculus, Algebra, Trigonometry, Hebrew numerals, Li Wang, Ashutosh Kumar, Andrea Medini

Click to edit the document details