c1ex5 - MAC2311 Final 1. Evaluate R 1 y ( y 2 + 1) 5 dy ....

Info iconThis preview shows pages 1–8. Sign up to view the full content.

View Full Document Right Arrow Icon

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

View Full DocumentRight Arrow Icon

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

View Full DocumentRight Arrow Icon

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

View Full DocumentRight Arrow Icon

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

View Full DocumentRight Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: MAC2311 Final 1. Evaluate R 1 y ( y 2 + 1) 5 dy . 2. Find the absolute max and min of f ( x ) = ( x 2 + 2 x ) 3 on the interval [- 3 , 3]. 1 3. Evaluate the limit: lim x → + x 2 ln x . 4. Find the shortest distance between the line y = 3 x + 2 and the point (1,1). 2 5. Find the derivative of y = 8 e sin θ . 6. Determine y given xy 4 + x 2 y = x + 3 y . 3 7. Find the equation of the tangent line to the function f ( x ) = x 2- 1 x 2 +1 at the point (0,-1). 8. Evaluate R π x + 2 cos x dx . 4 9. The area of a triangle increasing at a constant rate of 10 cm 2 /sec . Find dh dt if db dt = 2 cm/sec and b = 3 cm , h = 2 cm . 10. For the function f ( x ) = x x +8 find: intervals upon which the function is increasing and de- creasing; intervals upon which the function is concave upward and downward; local max and mins; inflection points; and vertical and horizontal asymptotes. Use this information to graph the function. 5 10. cont. 6 Solutions: 1. We begin with a substitution and choose u = y 2 + 1 so that du = 2 y dy or (1 / 2) du = y dy. Rewriting the integral we see R y ( y 2 + 1) 5 dy = R ( y 2 + 1) 5 ( y dy ) = R u 5 (1 / 2) du = (1 / 2) R u 5 du = (1 / 2)(1 / 6) u 6 = (1 / 12) u 6 = (1 / 12)( y 2 + 1) 6 . Therefore, R 1 y ( y 2 + 1) 5 dy = (1 / 12)( y 2 + 1) 6 | 1 = (1 / 12)((1) 2 + 1) 6- (1 / 12)((0) 2 + 1) 6 = (1 / 12)(64)...
View Full Document

This note was uploaded on 02/21/2010 for the course MAC 2311 taught by Professor All during the Spring '08 term at University of Florida.

Page1 / 10

c1ex5 - MAC2311 Final 1. Evaluate R 1 y ( y 2 + 1) 5 dy ....

This preview shows document pages 1 - 8. Sign up to view the full document.

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