INSTRUCTOR’S SOLUTIONS MANUAL
SECTION 2.1 (PAGE 100)
y
This is the line x C y D k if 2a D 1, and so k D .1=2/ C .1=2/2 D 3=4.
2
Full file at https://testbankuniv.eu/Calculus-Several-Variables-Canadian-9th-Edition-Adams-Solutions-Manual 24.
The curves y D kx 2 and y D k.x The slope of y D kx 2 at x D 1 is m1 D lim
h!0
k.1 C h/2 h
The slope of y D k.x m2 D lim
k.2
h!0
k
2/2 intersect at .1; k/.
1 -3
-2
-1
D lim .2 C h/k D 2k:
-2
2
2/ at x D 1 is k
D lim . 2 C h/k D h!0
x
2
-1
h!0
.1 C h//2 h
1 1j
x
-3 Fig. 2.1-27
2k:
The two curves intersect at right angles if 2k D 1=. 2k/, that is, if 4k 2 D 1, which is satisfied if k D ˙1=2.
y D jx 2
28.
25. Horizontal tangents at .0; 0/, .3; 108/, and .5; 0/. y .3; 108/
Horizontal tangent at .a; 2/ and . a; 2/ for all a > 1. No tangents at .1; 2/ and . 1; 2/. y y D jx C 1j jx 1j 2 1
100 80
-3
-2
-1
60
1
2
x
-1
40 y D x 3 .5
20 -1
1
2
-2
x/2
3
4
5
-3 Fig. 2.1-28
x
-20 Fig. 2.1-25 29. 26. Horizontal tangent at . 1; 8/ and .2; 19/. y
Horizontal tangent at .0; 1/. The tangents at .˙1; 0/ are vertical. y y D .x 2
20 . 1; 8/ 10 -2
-1
y D 2x 3
3x 2
1
2
1/1=3 2 1
12x C 1 3
-3
x
-2
-1
1
2
x
-1
-10 -2 -20
.2; 19/ -3 Fig. 2.1-29
-30 Fig. 2.1-26
27.
Horizontal tangent at . 1=2; 5=4/. No tangents at . 1; 1/ and .1; 1/.
30.
Horizontal tangent at .0; 1/. No tangents at . 1; 0/ and .1; 0/.
Copyright © 2018 Pearson Canada Inc.
Full file at https://testbankuniv.eu/Calculus-Several-Variables-Canadian-9th-Edition-Adams-Solutions-Manual
41