Pre-Calc Homework Solutions 62

Pre-Calc Homework Solutions 62 - 62 Section 2.4 (b) The...

Info iconThis preview shows page 1. Sign up to view the full content.

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

Unformatted text preview: 62 Section 2.4 (b) The slope of the tangent steadily decreases as a increases. 23. Let f (t) lim h0 17. continued 4 lim h0 f(2 h) h f(2) lim h0 (2 4 h) 1 2 lim h0 [4 h (2 h)] 4h 2 100 4.9t 2. f(2) f(2 Yes. The slope is 1 . 4 h lim h0 4h 1 4 3 4 3 4 2 2 lim h0 h) h [100 100 4.9(2 19.6 lim h0 h) 2] h 19.6h h [100 4.9h 2 4.9(2) 2] 100 19.6 18. No. The function is discontinuous at x because lim x(3 /4) lim ( 19.6 h0 4.9h) f(x) cos 3 4 lim x(3 /4) sin x 2 2 sin 19.6 The object is falling at a speed of 19.6 m/sec. but f 19. (a) 3 4 . [(a a2 2ah h h) 2 2ah h2 2] h h2 h (a 2 2 2) a2 2 lim h0 f(a h) h f(a) lim h0 24. Let f (t) lim h0 3t 2. h) h f(10) 60h h 3h 2 f(10 300 lim h0 lim h0 3(10 h) 2 h 300 lim h0 h0 lim h0 300 lim (2a 2a h) lim (60 h0 3h) 60 The rocket's speed is 60 ft/sec. 25. Let f(r) lim h0 (b) The slope of the tangent steadily increases as a increases. 2 2 20. (a) lim h0 f(a h) h f(a) lim h0 a h a r 2, the area of a circle of radius r. h) h f(3) lim h0 lim h0 h 2a 2(a h) ah(a h) 2 a(a h) f(3 lim h0 (3 9 lim h0 h0 h)2 h 6 h h (3)2 h2 9 2 a2 lim (6 6 h) (b) The slope of the tangent is always negative. The tangents are very steep near x 0 and nearly horizontal as a moves away from the origin. 21. (a) lim h0 The area is changing at a rate of 6 in2/in., that is, 6 square inches of area per inch of radius. 26. Let f (r) 4 3 r . 3 f(2 h) f(2) lim h h0 f(a h) h f(a) lim h0 a 1 h 1 1 a 1 h (a 1) (a h 1) 1)(a h 1) h0 h(a lim lim lim h0 4 (2 3 h)3 h h)3 h 12h 4 (2)3 3 h0 (a 1 1) 2 1 1)(a h 1) (a (b) The slope of the tangent is always negative. The tangents are very steep near x 1 and nearly horizontal as a moves away from the origin. 22. (a) lim h0 4 3 4 3 4 3 4 3 lim h0 (2 8 23 6h 2 + h 3 h 8 lim h0 lim (12 h0 6h h 2) 12 f(a h) h f(a) lim h0 [9 9 (a a2 lim h0 lim h0 h0 2ah h h)2] (9 h 2ah h 2 h h2 a 2) 9 a2 16 The volume is changing at a rate of 16 in3/in., that is, 16 cubic inches of volume per inch of radius. lim ( 2a 2a h) ...
View Full Document

This note was uploaded on 10/05/2011 for the course MAC 1147 taught by Professor German during the Spring '08 term at University of Florida.

Ask a homework question - tutors are online