Pre-Calc Homework Solutions 61

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

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: 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] ...
View Full Document

Ask a homework question - tutors are online