lim2. 1 aSolution: The limit of the given function in the numerator and denominator is 0which implies that it has in connection with indeterminate forms. By applyingthe 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 theconjugateApply sum and difference in multiplying the expres-sions in the numerator243-4-1)(+2)Simplify the expression with exponent in the numeratorNG ESimplify 3-4 = -1(2)Cancel xe - 1Therefore,+3-22-1linm+2)ELeaning Task 3: Evaluate the limits of the given exponential, logarithmic andtrigonometric function ( m items 8– 10 15 in radian measure)lim(3-3+5)1. 4ALASElim (in 2x + 5) + 46. **lim(125-++2)lim log:(x-8x -1)2. *-57. *+5Him+lim 4 sin(x +7) +38.3. 1lim4. 3lim cos++9. atSar+2lim loglim tanG+5++65.10.Learning Task 4: Evaluate the limit of a function using the concept of special lim-its.sintlimlim2.1. 0tlim3. -0ainelimlim5. 0PIVOT 4A CALABARZON22

We have to find the following given limits

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) +

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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Estimation

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Question

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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