Calculus: BasicTechniquesforFindingLimits by: javier
Calculus: Basic Techniques for Finding Limits
by: javier
Basic Techniques for Finding Limits By Graphing
Basic Techniques for Finding Limits: By Graphing
□
lim xx
x→0+
1.5
1
0.5 0
1
2
3
4
Basic Techniques for Finding Limits: By Graphing
□
lim xx
x→0+
1.5
1
0.5 0
1
2
3
4
Basic Techniques for Finding Limits: By Graphing
□
lim xx
x→0+
1.5
1
0.5
□
lim
x→2−
ln(x) − ln(2) x−2
0
1
2
3
4
Basic Techniques for Finding Limits: By Graphing
□
lim xx
x→0+
1.5
□
lim
x→2−
ln(x) − ln(2) x−2
1
0.5
□
lim
x→2+
ln(x) − ln(2) x−2
0
1
2
3
4
Basic Techniques for Finding Limits: By Graphing
□
lim xx
x→0+
ln(x) − ln(2) □ lim − x−2 x→2
1.5
1
□
lim
x→2+
□ lim
x→2
ln(x) − ln(2) x−2
ln(x) − ln(2) x−2
0.5 0
1
2
3
4
Basic Techniques for Finding Limits By Engineer’s Method
Basic Techniques for Finding Limits: By Engineer’s Method
□
lim xx ( ) 2 x □ lim 1 + x→∞ x cos(x) − cos(π) □ lim + x−π x→π x→0+
Basic Techniques for Finding Limits by Re-Write Method
Basic Techniques for Finding Limits: by Re-Write Method
x−3 √ □ lim √ x→3 x− 3
Basic Techniques for Finding Limits: by Re-Write Method
x−3 √ □ lim √ x→3 x− 3 1 + x + x2 □ lim x→∞ 3 − 7x + 5x3
Basic Techniques for Finding Limits: by Re-Write Method
x−3 √ □ lim √ x→3 x− 3 1 + x + x2 □ lim x→∞ 3 − 7x + 5x3 1 + x + x2 □ lim x→∞ 3 − 7x + 5x2
Basic Techniques for Finding Limits: by Re-Write Method
x−3 √ □ lim √ x→3 x− 3 1 + x + x2 □ lim x→∞ 3 − 7x + 5x3 1 + x + x2 □ lim x→∞ 3 − 7x + 5x2 1 + x + x3 □ lim x→∞ 3 − 7x + 5x2
Basic Techniques for Finding Limits by Recognizing Famous Limits
Basic Techniques for Finding Limits: by Recognizing Famous Limits □
lim xx
x→0+
Basic Techniques for Finding Limits: by Recognizing Famous Limits □
lim xx ( ) 1 x □ lim 1 + x→∞ x x→0+
Basic Techniques for Finding Limits: by Recognizing Famous Limits □
lim xx ( □ lim 1 + x→∞ ( □ lim 1 + x→0+
x→∞
) 1 x x ) −3 x x
Basic Techniques for Finding Limits: by Recognizing Famous Limits □
lim xx ( □ lim 1 + x→∞ ( □ lim 1 + x→0+
x→∞
sin(x) x→0 x
□ lim
) 1 x x ) −3 x x
Basic Techniques for Finding Limits: by Recognizing Famous Limits □
lim xx ( □ lim 1 + x→∞ ( □ lim 1 + x→0+
x→∞
) 1 x x ) −3 x x
sin(x) x→0 x 1 − cos(x) □ lim x→0 x □ lim
Basic Techniques for Finding Limits: by Recognizing Famous Limits □
lim xx ( □ lim 1 + x→∞ ( □ lim 1 + x→0+
x→∞
) 1 x x ) −3 x x
sin(x) x→0 x 1 − cos(x) □ lim x→0 x □ lim (.9999)x □ lim
x→∞
Basic Techniques for Finding Limits: by Recognizing Famous Limits □
lim xx ( □ lim 1 + x→∞ ( □ lim 1 + x→0+
x→∞
) 1 x x ) −3 x x
sin(x) x→0 x 1 − cos(x) □ lim x→0 x □ lim (.9999)x □ lim
x→∞
□ lim (1.00001)x x→∞
Basic Techniques for Finding Limits: by Recognizing Famous Limits □
lim xx ( □ lim 1 + x→∞ ( □ lim 1 + x→0+
x→∞
) 1 x x ) −3 x x
sin(x) x→0 x 1 − cos(x) □ lim x→0 x □ lim (.9999)x □ lim
x→∞
□ lim (1.00001)x x→∞
ln(x) x→∞ x
□ lim
Basic Techniques for Finding Limits by Plug-In-Method
Basic Techniques for Finding Limits: by Plug-In-Method
□ lim (3x + 3) x→5 ) ( 1 □ lim 5 + x→∞ x
Basic Techniques for Finding Limits by Using Computers
Basic Techniques for Finding Limits: by Using Computers
LIMITS
SAGEMATH
by: javier
Basic Techniques for Finding Limits By Graphing
Basic Techniques for Finding Limits: By Graphing
□
lim xx
x→0+
1.5
1
0.5 0
1
2
3
4
Basic Techniques for Finding Limits: By Graphing
□
lim xx
x→0+
1.5
1
0.5 0
1
2
3
4
Basic Techniques for Finding Limits: By Graphing
□
lim xx
x→0+
1.5
1
0.5
□
lim
x→2−
ln(x) − ln(2) x−2
0
1
2
3
4
Basic Techniques for Finding Limits: By Graphing
□
lim xx
x→0+
1.5
□
lim
x→2−
ln(x) − ln(2) x−2
1
0.5
□
lim
x→2+
ln(x) − ln(2) x−2
0
1
2
3
4
Basic Techniques for Finding Limits: By Graphing
□
lim xx
x→0+
ln(x) − ln(2) □ lim − x−2 x→2
1.5
1
□
lim
x→2+
□ lim
x→2
ln(x) − ln(2) x−2
ln(x) − ln(2) x−2
0.5 0
1
2
3
4
Basic Techniques for Finding Limits By Engineer’s Method
Basic Techniques for Finding Limits: By Engineer’s Method
□
lim xx ( ) 2 x □ lim 1 + x→∞ x cos(x) − cos(π) □ lim + x−π x→π x→0+
Basic Techniques for Finding Limits by Re-Write Method
Basic Techniques for Finding Limits: by Re-Write Method
x−3 √ □ lim √ x→3 x− 3
Basic Techniques for Finding Limits: by Re-Write Method
x−3 √ □ lim √ x→3 x− 3 1 + x + x2 □ lim x→∞ 3 − 7x + 5x3
Basic Techniques for Finding Limits: by Re-Write Method
x−3 √ □ lim √ x→3 x− 3 1 + x + x2 □ lim x→∞ 3 − 7x + 5x3 1 + x + x2 □ lim x→∞ 3 − 7x + 5x2
Basic Techniques for Finding Limits: by Re-Write Method
x−3 √ □ lim √ x→3 x− 3 1 + x + x2 □ lim x→∞ 3 − 7x + 5x3 1 + x + x2 □ lim x→∞ 3 − 7x + 5x2 1 + x + x3 □ lim x→∞ 3 − 7x + 5x2
Basic Techniques for Finding Limits by Recognizing Famous Limits
Basic Techniques for Finding Limits: by Recognizing Famous Limits □
lim xx
x→0+
Basic Techniques for Finding Limits: by Recognizing Famous Limits □
lim xx ( ) 1 x □ lim 1 + x→∞ x x→0+
Basic Techniques for Finding Limits: by Recognizing Famous Limits □
lim xx ( □ lim 1 + x→∞ ( □ lim 1 + x→0+
x→∞
) 1 x x ) −3 x x
Basic Techniques for Finding Limits: by Recognizing Famous Limits □
lim xx ( □ lim 1 + x→∞ ( □ lim 1 + x→0+
x→∞
sin(x) x→0 x
□ lim
) 1 x x ) −3 x x
Basic Techniques for Finding Limits: by Recognizing Famous Limits □
lim xx ( □ lim 1 + x→∞ ( □ lim 1 + x→0+
x→∞
) 1 x x ) −3 x x
sin(x) x→0 x 1 − cos(x) □ lim x→0 x □ lim
Basic Techniques for Finding Limits: by Recognizing Famous Limits □
lim xx ( □ lim 1 + x→∞ ( □ lim 1 + x→0+
x→∞
) 1 x x ) −3 x x
sin(x) x→0 x 1 − cos(x) □ lim x→0 x □ lim (.9999)x □ lim
x→∞
Basic Techniques for Finding Limits: by Recognizing Famous Limits □
lim xx ( □ lim 1 + x→∞ ( □ lim 1 + x→0+
x→∞
) 1 x x ) −3 x x
sin(x) x→0 x 1 − cos(x) □ lim x→0 x □ lim (.9999)x □ lim
x→∞
□ lim (1.00001)x x→∞
Basic Techniques for Finding Limits: by Recognizing Famous Limits □
lim xx ( □ lim 1 + x→∞ ( □ lim 1 + x→0+
x→∞
) 1 x x ) −3 x x
sin(x) x→0 x 1 − cos(x) □ lim x→0 x □ lim (.9999)x □ lim
x→∞
□ lim (1.00001)x x→∞
ln(x) x→∞ x
□ lim
Basic Techniques for Finding Limits by Plug-In-Method
Basic Techniques for Finding Limits: by Plug-In-Method
□ lim (3x + 3) x→5 ) ( 1 □ lim 5 + x→∞ x
Basic Techniques for Finding Limits by Using Computers
Basic Techniques for Finding Limits: by Using Computers
LIMITS
SAGEMATH
