lim ution: The limit of the given function in the numerato ch implies that it has in connection with indetermin concept of rationalizing the numerator, (note that ra d in the numerator or denominator where the radical Multiply both numerator and o conjugate Apply sum and difference in m sions in the numerator 241-4 Simplify the expression with expo NG E Simplify 3 -4 = -1 +3+2) refore, Cancel x -1 Vx+3-2 x2-1 ning Task 3: Evaluate the limits of the given expo nometric function1 lim(33+5) e in items 8- 10 15 in radian measu: BA lim (in 2x + 5) +

Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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lim
2. 1 a
Solution: The limit of the given function in the numerator and denominator is 0
which implies that it has in connection with indeterminate forms. By applying
the concept of rationalizing the numerator, (note that rationalization can be ap-
plied in the numerator or denominator where the radical expression located)
Multiply both numerator and denominator by the
conjugate
Apply sum and difference in multiplying the expres-
sions in the numerator
243-4
-1)(+2)
Simplify the expression with exponent in the numerator
NG E
Simplify 3-4 = -1
(2)
Cancel xe - 1
Therefore,
+3-2
2-1
linm
+2)
E
Leaning Task 3: Evaluate the limits of the given exponential, logarithmic and
trigonometric function ( m items 8– 10 15 in radian measure)
lim(3-3+5)
1. 4
ALASE
lim (in 2x + 5) + 4
6. **
lim(125-+
+2)
lim log:(x-8x -1)
2. *-5
7. *+5
Him+
lim 4 sin(x +7) +3
8.
3. 1
lim
4. 3
lim cos++
9. at
Sar+2
lim log
lim tanG+5+
+6
5.
10.
Learning Task 4: Evaluate the limit of a function using the concept of special lim-
its.
sint
lim
lim
2.
1. 0t
lim
3. -0
aine
lim
lim
5. 0
PIVOT 4A CALABARZON
22
Transcribed Image Text:lim 2. 1 a Solution: The limit of the given function in the numerator and denominator is 0 which implies that it has in connection with indeterminate forms. By applying the concept of rationalizing the numerator, (note that rationalization can be ap- plied in the numerator or denominator where the radical expression located) Multiply both numerator and denominator by the conjugate Apply sum and difference in multiplying the expres- sions in the numerator 243-4 -1)(+2) Simplify the expression with exponent in the numerator NG E Simplify 3-4 = -1 (2) Cancel xe - 1 Therefore, +3-2 2-1 linm +2) E Leaning Task 3: Evaluate the limits of the given exponential, logarithmic and trigonometric function ( m items 8– 10 15 in radian measure) lim(3-3+5) 1. 4 ALASE lim (in 2x + 5) + 4 6. ** lim(125-+ +2) lim log:(x-8x -1) 2. *-5 7. *+5 Him+ lim 4 sin(x +7) +3 8. 3. 1 lim 4. 3 lim cos++ 9. at Sar+2 lim log lim tanG+5+ +6 5. 10. Learning Task 4: Evaluate the limit of a function using the concept of special lim- its. sint lim lim 2. 1. 0t lim 3. -0 aine lim lim 5. 0 PIVOT 4A CALABARZON 22
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