Pre-Calc Homework Solutions 225

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

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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 ...
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