LimitCalc1.nb
FullSimplify @D@Sqrt@5 x ^ 2 + 2D  Hx - 2L, xDD
-
2 H1 + 5 xL
H- 2 + xL2
2 + 5 x2
Solve@D@Sqrt@5 x ^ 2 + 2D  Hx - 2L, xD Š 0, xD
::x ® -
1
5
>>
FullSimplify @D@Sqrt@5 x ^ 2 + 2D  Hx - 2L, 8x, 2<DD
48 + 10 x2 H3 + 10 xL
H- 2 + xL3 I2 + 5 x2 M
32
Solve@D@Sqrt@5 x ^ 2 + 2D  Hx - 2L, 8x, 2<D Š 0, xD  N
88x ® - 0.896813<, 8x ® 0.298406 + 0.667969 ä<, 8x ® 0.298406 - 0.667969 ä<<
PlotA48 + 10 x2 H3 + 10 xL, 8x, - 1, 1<E
150
100
50
-1.0
-0.5
0.5
1.0
Sqrt@5 x ^ 2 + 2D  Hx - 2L . x ® H- 1  5L
5
11
Sqrt@5 x ^ 2 + 2D  Hx - 2L . x ®
1
1
-1 -
10
J241 - 44
- 0.847085
Limit@Sqrt@5 x ^ 2 + 2D  Hx - 2L, x ® InfinityD
5
Limit@Sqrt@5 x ^ 2 + 2D  Hx - 2L, x ® - InfinityD
-
5
30 N
13
- J241 - 44
30 N
13
 N
1
LimitCalc1.nb
In[6]:=
Plot@8Sqrt@5 x ^ 2 + 2D  Hx - 2L, Sqrt@5D, - Sqrt@5D<, 8x, - 10, 10<D
5
Out[6]=
-10
-5
5
-5
10
2