Pre-Calc Homework Solutions 61

Pre-Calc Homework Solutions 61 - Section 2.4 1 h 1 1 2 1 61...

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Unformatted text preview: Section 2.4 1 h) 1 1 2 1 61 13. (a) Near x lim h0 2, f (x) h) h f(2) x x. lim h0 11. (a) lim h0 y(2 h) h y(2) lim h0 (2 h 1 h 1 f(2 (2 h) h 2 lim 1 h0 1 1 (b) Near x lim h0 3, f(x) h) h x lim h0 x. (3 h) h 3 lim h0 h 1 (h 1) h(h 1) 1 h 1 f( 3 f( 3) lim h0 lim h0 1 1 x 2 lim h0 14. Near x lim f(1 1, f (x) f(1) 1 (x [2 (1 2) h)] h 2 (2 x. 1) lim h0 1 (b) The tangent line has slope (2, y(2)) (2, 1). y (x 2) 1 y x 3 (c) The normal line has slope through (2, y(2)) y y (d) 1(x x 1 2) 1 (2, 1). 1 and passes through h0 h) h 1 h lim h h0 lim h0 1 1 15. First, note that f (0) lim h0 2. lim h0 f(0 h) h f(0) (2 2h 2h h h h2 h 2) 2 1 1 1 and passes lim h0 h0 lim ( 2 2 lim h0 h) f(0 h) h f(0) lim h0 h0 (2h 2) h 2 lim 2 2 [ 4.7, 4.7] by [ 3.1, 3.1] 12. (a) lim h0 y(0 h) h y(0) lim h0 (h2 h2 h 3h h 3h 1) ( 1) No, the slope from the left is 2 and the slope from the right is 2. The two-sided limit of the difference quotient does not exist. 16. First, note that f(0) lim h0 0. lim h0 lim h0 h0 f (0 f(0 lim (h 3 (b) The tangent line has slope (0, y(0)) y y 3(x 3x (0, 0) 1 1 3 3) lim h0 h) h h) h f (0) f(0) h h (h2 0 h) h 0 1 lim h0 lim (h h0 1) 1 1. 1 2 1 1 2 3 and passes through Yes. The slope is 17. First, note that f (2) lim h0 1). 1 f(2 h) h f(2) lim h0 2 h lim h0 (c) The normal line has slope through (0, y(0)) y y (d) 1 (x 3 1 x 3 1 and passes 3 lim h0 (0, 1). = lim h0 h 2 (2 h) 2h(2 h) h 2h(2 h) 1 2(2 h) 0) 1 1 1 4 [ 6, 6] by [ 5, 3] ...
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