1. Evalué el límite si existe
h 5 lim h 0
2
25
h
Solución
h 5 lim
2
25
h 2 10h 25 25 lim h 0 h 0 h h 2 h h 10 h 10h lim lim lim h 10 h 0 h 0 h 0 h h lim h 10 0 10 10 h 0
limit
IIh-5M^2-25M h
• function to find limit of: • value to approach:
0
Also include: specify variable
Limit:
Hh - 5L - 25
È specify direction È include second limit Step-by-step solution
2
lim h®0
h
- 10
Plot: -6
-4
-2
2
4
6
-5
-10
Hh from -6 to 6L
-15
Series expansion at h=0:
h - 10
Generated by Wolfram|Alpha (www.wolframalpha.com) on February 9, 2014 from Champaign, IL. © Wolfram Alpha LLC— A Wolfram Research Company
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1 1 x 2 lim x2 x 2 Solución
1 1 2 x x 2 2 x lim x 2 lim 2 x lim lim x 2 x 2 x 2 x 2 x 2 2 x x 2 x 2 2 x x 2 1 1 x 2 2 x 4
lim
limit
• function to find limit of: • value to approach:
I1 x-1 2M Ix-2M 2
È specify direction È include second limit
Also include: specify variable
Limit:
Approximate form
lim x®2
1 x
-
1 2
x-2
-
Step-by-step solution
1 4
Plot: 1.5
2.0
2.5
3.0
-0.2 Hx from 1 to 3L
-0.3 -0.4 -0.5
Series expansion at x=2: 1 4
- +
x-2 8
-
1 16
Hx - 2L2 +
1 32
Hx - 2L3 -
1 64
Hx - 2L4 +
1 128
Hx - 2L5 + OIHx - 2L6 M
Generated by Wolfram|Alpha (www.wolframalpha.com) on February 9, 2014 from Champaign, IL. © Wolfram Alpha LLC— A Wolfram Research Company
More terms
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2. Encuentre el límite si existe. Si no lo hay explique porque
1 1 lim x 0 x x Solución Tenemos que
x, si x 0 x x si x 0
1 1 2 1 1 lim lim lim No existe x 0 x x x 0 x x x 0 x
x2 1 3. Sea F ( x ) x 1 a. Hallar i. lim F ( x) x1
Solución x2 1 x2 1 lim lim lim x 1 2 x 1 x 1 x 1 x 1 x 1 ii.
lim F ( x) x1
Solución x2 1 x2 1 lim lim lim x 1 2 x 1 x 1 x 1 x 1 x 1 b. ¿Existe lim F ( x) x1
Solución El lim F ( x) no existe debido a que lim F ( x) lim F ( x) x1
c. Trazar la gráfica de F ( x) Solución
x1
x1
limit
• function to find limit of: • value to approach:
Ix^2-1M x-1 1
Also include: specify variable
È specify direction È include second limit
Input:
x2 - 1
lim x®1
x - 1¤
z¤ is the absolute value of z »
Limit:
Htwo-sided limit does not existL
One-sided limits:
x2 - 1
lim-
x®1
x - 1¤ x2 - 1
lim x®1+
Plot:
x - 1¤
-2 2
4 3 2 1 -1
1
2
3
Hx from -1 to 3L
-1 -2
Series expansion at x=1: Hx-1L2 +2 Hx-1L x-1¤
Generated by Wolfram|Alpha (www.wolframalpha.com) on February 9, 2014 from Champaign, IL. © Wolfram Alpha LLC— A Wolfram Research Company
1
4. Halle el limite trigonométrico
sen 0 tan
a. lim
Solución
lim
sen
sen sen 0 lim 0 tan 0 sen 1 sen 1 1 1 lim lim 0 cos 0 cos 1 1 1 1 1 2 lim
limit
• function to find limit of:
senx Hx+tanxL
• value to approach:
0
Also include: specify variable
È specify direction È include second limit
Limit:
Approximate form
sinHxL lim x®0
x + tanHxL
Step-by-step solution
1 2
Plot: 1.0 0.5
-6
-4
-2
2
4
6
-0.5
Hx from -6 to 6L
-1.0
Series expansion at x=0: 1 2
-
x2 6
-
x4 720
More terms
+ OIx 6 M
Generated by Wolfram|Alpha (www.wolframalpha.com) on February 9, 2014 from Champaign, IL. © Wolfram Alpha LLC— A Wolfram Research Company
1
cot 2 x x0 csc x
b. lim
Solución
cos 2 x cos 2 x cot 2 x lim lim sen2 x lim 2senx cosx x 0 csc x x 0 x 0 1 1 senx senx senx cos 2 x cos 2 x cos 2 0 1 lim lim x 0 2 senx cos x x 0 2cos x 2cos 0 2
limit
• function to find limit of:
cot2x cscx
• value to approach:
0
Also include: specify variable
È specify direction È include second limit
Limit:
Approximate form
cotH2 xL lim x®0
cscHxL
Step-by-step solution
1 2 cotHxL is the cotangent function » cscHxL is the cosecant function »
Plot: 2 1
-6
-4
-2
2
4
6
-1
Hx from -6 to 6L
-2
Series expansion at x=0: 1 2
-
3x 4
2
4
-
x 16
6
-
7x 160
More terms
+ OIx 7 M
Generated by Wolfram|Alpha (www.wolframalpha.com) on February 9, 2014 from Champaign, IL. © Wolfram Alpha LLC— A Wolfram Research Company
1