# 119Mdt2 - 2 dx(b 2 π Z p | sin θ | 119 | sin θ | 1cos...

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

Last Name Name Student No.: Department: Section: Signature: : : : : : : : : : : Code Acad.Year Semester Date Time Duration M E T U Northern Cyprus Campus Calculus and Analytical Geometry II. Midterm Math 119 2007-2008 Fall 9.12.2007 10:00 120 minutes 6 QUESTIONS ON 6 PAGES TOTAL 100 POINTS 1 2 3 4 5 6 1. (5+5+5+5=20 points) Let f ( x ) = x 2 + 4 x 2 - 4 (a) Find the domain of f and its asymptotes, if any. (b) Find the critical points of f , if any. (c) Determine the intervals where f is concave up/down. (d) Sketch the graph of f .

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

View Full Document
2. (10 points) Find the area of the largest rectangle that can be inscribed in a right triangle with perpendicular sides of length 3 cm and 4 cm , if the two sides of the rectangle lie along these sides of the triangle.
3. (5+5+5=15 points) Evaluate each of the following integrals. (a) Z x 3 (2 x 4 + 7)

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

View Full Document

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.

Unformatted text preview: 2 dx (b) 2 π Z p | sin θ | 119 + | sin θ | + 1cos θdθ (c) 2 Z 1 ( x + 1 x ) 2 dx 4. (a) (10 points) If f ( x ) is diﬀerentiable, and x Z f ( t ) dt = f ( x ) 2 for all x , ﬁnd f ( x ). (b) (10 points) Find F ( x ) if F ( x ) = 2 x Z x tdt t 3 + 1 dt 5. (5+10=15 points) (a) Sketch the region enclosed by y = | x | and y = x 2-1. (b) Find the area of the region. 6. (a) (10 points) Find the volume of the solid obtained by rotating the area bounded by y = sec x , y = 0, x = 0 and x = π/ 3 around the x-axis. (b) (10 points) Find the volume of the solid obtained by rotating the area bounded by y = 1 (1 + x 2 ) 2 , y = 0, x = 1 and x = 2 around the y-axis....
View Full Document

{[ snackBarMessage ]}

### Page1 / 6

119Mdt2 - 2 dx(b 2 π Z p | sin θ | 119 | sin θ | 1cos...

This preview shows document pages 1 - 6. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online