Pre-Calc Homework Solutions 225

# Pre-Calc Homework Solutions 225 - Section 5.5 4 Substitute...

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

This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: Section 5.5 4. Substitute the expression in step 2 for the parenthetically enclosed expression in step 3: Ap h (2Ah 2 6C) 3 h (y 4y1 y2). 3 0 225 Section 5.5 Exercises 1. (a) f (x) x f (x) x, h 0 0 2 4 1 2 1 2 0 1 2 1 1 Quick Review 5.5 1. y sin x y cos x y 0 on [ 1, 1], so the curve is concave down on [ 1, 1]. 2. y y y 4x 12 12x 2 0 on [8, 17], so the curve is concave up on [8, 17]. 3 3 2 3 2 2 2 3 2 T 1 0 4 2 1 2 2(1) 2 2 2 (b) f (x) 1, f (x) 0 The approximation is exact. 2 (c) 0 x dx 1 2 x 2 2 2 0 3. y 12x 2 6x y 24x 6 y 0 on [ 8, 0], so the curve is concave down on [ 8, 0]. 4. y y y 1 x cos 2 2 1 x sin 4 2 2. (a) f (x) x f (x) T x 2, h 0 0 2 2 4 1 2 1 4 1 4 0 1 2 1 1 2(1) 3 2 9 4 2 4 9 4 1 0 4 2 4 2.75 0 on [48 , 50 ], so the curve is concave down on (b) f (x) 2x, f (x) 2 0 on [0, 2] The approximation is an overestimate. 2 [48 , 50 ]. 5. y y y 6. y y y 2e 4e 2x 0 on [ 5, 5], so the curve is concave up on [ 5, 5]. 1 x 1 x2 2x (c) 0 x 2 dx x ,h 0 0 3 1 3 x 3 2 0 8 3 0 4 1 2 3. (a) f (x) x f (x) 2 0 on [100, 200], so the curve is concave down on T 1 0 4 1 2 1 8 1 1 3 2 27 8 2 8 27 8 [100, 200]. 7. y y y 8. y y y 1 x2 2 x3 2 1 8 2(1) 2 8 4.25 (b) f (x) 3x 2, f (x) 6x 0 on [0, 2] The approximation is an overestimate. 2 (c) 0 x 3 dx 1 ,h x 0 on [3, 6], so the curve is concave up on [3, 6]. csc x cot x ( csc x)( csc2 x) (csc x cot x)(cot x) csc3 x csc x cot2 x 0 on [0, ], so the curve is concave up on [0, ]. 1 4 x 4 2 2 4 0 4. (a) f (x) x f (x) T (b) f (x) 1 4 3 2 2 3 1 4 7 4 4 7 1 1 2 9. y 100x 9 y 900x 8 y 0 on [10, 1010], so the curve is concave down on [10, 1010]. 10. y y y cos x sin x sin x cos x 0 on [1, 2], so the curve is concave down. 5 4 4 5 4 5 2 1 2 4 7 1 2 1 1 8 2 1 , f (x) x2 2 3 2 x3 2 0.697 0 on [1, 2] The approximation is an overestimate. 2 (c) 1 1 dx x 2 ln x 1 ln 2 0.693 ...
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