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Math
Calculus
CALCULUS, EARLY TRANSITIONS (LL)
Chapter 2.3, Problem 49E
Chapter 2.3, Problem 49E
BUY
CALCULUS, EARLY TRANSITIONS (LL)
9th Edition
ISBN:
9780357305041
Author: Stewart
Publisher:
CENGAGE L
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1 Functions And Models
2 Limits And Derivatives
3 Differentiation Rules
4 Applications Of Differentiation
5 Integrals
6 Applications Of Integration
7 Techniques Of Integration
8 Further Applications Of Integration
9 Differential Equations
10 Parametric Equations And Polar Coordinates
11 Sequences, Series, And Power Series
12 Vectors And The Geometry Of Space
13 Vector Functions
14 Partial Derivatives
15 Multiple Integrals
16 Vector Calculus
A Numbers, Inequalities, And Absolute Values
B Coordinate Geometry And Lines
C Graphs Of Second-degree Equations
D Trigonometry
E Sigma Notation
F Proofs Of Theorems
G The Logarithm Defined As An Integral
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2.1 The Tangent And Velocity Problems
2.2 The Limit Of A Function
2.3 Calculating Limits Using The Limit Laws
2.4 The Precise Definition Of A Limit
2.5 Continuity
2.6 Limits At Infinity; Horizontal Asymptotes
2.7 Derivatives And Rates Of Change
2.8 The Derivative As A Function
Chapter Questions
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Problem 1E: Given that limx2f(x)=4limx2g(x)=2limx2h(x)=0 find the limits that ex.ist. If the limit does not...
Problem 2E: Tire graphs of f and g are given. Use them to evaluate each limit, if it exists. If the limit does...
Problem 3E: Evaluate the limit and justify each step by indicating the appropriate Limit Law(s). 3. limx54x25x
Problem 4E: Evaluate the limit and justify each step by indicating the appropriate Limit Law(s). 4....
Problem 5E: Evaluate the limit and justify each step by indicating the appropriate Limit Law(s). 5....
Problem 6E: Evaluate the limit and justify each step by indicating the appropriate Limit Law(s). 6....
Problem 7E: Evaluate the limit and justify each step by indicating the appropriate Limit Law(s). 7. limu29u3+2u2
Problem 8E: Evaluate the limit and justify each step by indicating the appropriate Limit Law(s). 8....
Problem 9E: Evaluate the limit and justify each step by indicating the appropriate Limit Law(s). 9....
Problem 10E: (a) What is wrong with the following equation? x2+x6x2=x+3 (b) In view of part (a). explain why the...
Problem 11E: Evaluate the limit, if it exists. 11. limx2(3x7)
Problem 12E: Evaluate the limit, if it exists. 12. limx6812x
Problem 13E: Evaluate the limit, if it exists. 13. limt4t22t8t4
Problem 14E: Evaluate the limit, if it exists. limx4x2+3xx2x12
Problem 15E: Evaluate the limit, if it exists. 15. limx2x2+5x+4x2
Problem 16E: Evaluate the limit, if it exists. 16. limx4x2+3xx2x12
Problem 17E: Evaluate the limit, if it exists. 17. limx2x2x63x2+5x2
Problem 18E: Evaluate the limit, if it exists. 18. limx52x2+9x5x225
Problem 19E: Evaluate the limit, if it exists. 19. limt3t327t29
Problem 20E: Evaluate the limit, if it exists. 20. limu1u+1u3+1
Problem 21E: Evaluate the limit, if it exists. 21. limh0(h3)29h
Problem 22E: Evaluate the limit, if it exists. 22. limx99x3x
Problem 23E: Evaluate the limit, if it exists. 23. limh09+h3h
Problem 24E: Evaluate the limit, if it exists. 24. limx22xx+22
Problem 25E: Evaluate the limit, if it exists. 25. limx31x13x3
Problem 26E: Evaluate the limit, if it exists. 26. limh0(2+h)1+21h
Problem 27E: Evaluate the limit, if it exists. 27. limt01+t1tt
Problem 28E: Evaluate the limit, if it exists. 28. limt01t1t2+t
Problem 29E: Evaluate the limit, if it exists. 29. limx164x16xx2
Problem 30E: Evaluate the limit, if it exists. 30. limx2x24x+4x43x24
Problem 31E: Evaluate the limit, if it exists. 31. limt01t1+t1t
Problem 32E: Evaluate the limit, if it exists. 32. limx4x2+95x+4
Problem 33E: Evaluate the limit, if it exists. limh0(x+h)x3h
Problem 34E: Evaluate the limit, if it exists. limh01(xh)21x2h
Problem 35E: (a) Estimate the value of limx0x1+3x1 by graphing the function f(x)=x/(1+3x1). (b) Make a table of...
Problem 36E: (a) Use a graph of f(x)=3+x3x to estimate the value of limx0f(x) to two decimal places. (b) Use a...
Problem 37E: Use the Squeeze Theorem to show that limx0x2cos20x=0 Illustrate by graphing the functions f(x)=x2 ,...
Problem 38E: Use the Squeeze Theorem to show that limx0x3+x2sinx=0 Illustrate by graphing the functions f, q, and...
Problem 39E: If 4x 9 f(x) x2 4x + 7 for x 0, find limx4f(x)
Problem 40E: If 2x g(x) x4 x2 + 2 for all x, evaluate limx1g(x)
Problem 41E: Prove that limx0x4cos2x=0.
Problem 42E: Prove that limxxesin(/x)=0.
Problem 43E: Find the limit, if it exists. If the limit does not exist, explain why. 43. lim x4 (x+42x)
Problem 44E: Find the limit, if it exists. If the limit does not exist, explain why. 44. limx4x+42x+8
Problem 45E: Find the limit, if it exists. If the limit does not exist, explain why. limx0.52x12x3x2
Problem 46E: Find the limit, if it exists. If the limit does not exist, explain why. limx22x2+x
Problem 47E: Find the limit, if it exists. If the limit does not exist, explain why. limx(1x1x)
Problem 48E: Find the limit, if it exists. If the limit does not exist, explain why. limx0+(1x1x)
Problem 49E
Problem 50E
Problem 51E: Let g(x)=x2+x6x2 (a) Find (i) limx2+g(x) (ii) limx2g(x) (b) Does limx2 g(x) exist'! (c) Sketch the...
Problem 52E: Let f(x)={x2+1ifx1(x2)2ifx1 (a) Find limx0 f(x).and lim x0+ f(x) (b) Does limx0 f(x) exist? (c)...
Problem 53E: Let B(t)={412tift2t+cift2 Find the value of c so that limt2B(t) exists.
Problem 54E: l.et g(x)={xifx13ifx=12xif1x2x3ifx2 (a) Evaluate each of the following, if it exists. (i) limx1g(x)...
Problem 55E: (a) If the symbol denotes the greatest integer function defined in Example I 0, evaluate (i)...
Problem 56E: Let f(x)=cosx,x. (a) Sketch the graph of f. (b) Evaluate each limit, if it exists. (i) limx0f(x)...
Problem 57E: If f(x)=x+x, show that lim x0 f(x) exists hut is not equal to f(2).
Problem 58E: In the theory of relativity, the Lorentz contraction formula L=L01v2/c2 expresses the length L of an...
Problem 59E: If p is a polynomial, Show that limxa p(x) = p(a)
Problem 60E
Problem 61E: If limx1f(x)8x1=10, find limx1f(x).
Problem 62E: If limx0f(x)x2=5, find the following limits. (a) limx0f(x) (b) limx0f(x)x
Problem 63E: If f(x)={x2ifxisrational0ifxisirrational prove that limx0f(x)=0.
Problem 64E: Show by means of an example that limxa[f(x)+g(x)] may exist even though neither...
Problem 65E: Show by means of an example that limxa[f(x)g(x)] may exist even though neither limxa f(x) nor limxa...
Problem 66E: Evaluate limx26x23x1.
Problem 67E: Is there a number a such that limx23x2+ax+a+3x2+x2 exists? If so, find the value of a and the value...
Problem 68E
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