By Mark McKibben

Designed for these looking support learning calculus in class - additionally beneficial for adults trying to learn/re-learn calculus. A source for teachers supplementing their guide. 501 Calculus difficulties is helping clients organize for educational assessments and construct problem-solving talents. not like textbooks, complete resolution reasons are supplied for all difficulties. contains: - Questions overlaying all of unmarried variable calculus - universal calculus blunders - certain answers/fully labored recommendations - thesaurus and theorem checklist - entry to loose on-line try out

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**Extra resources for 501 Calculus Questions**

**Sample text**

Properties of Absolute Value 1. a = b if and only if a = ±b . 2. a = b if and only if a = ±b . 3. a ≥ c if and only if a ≥ c or a ≤ − c . 4. a < c if and only if − c < a < c. Questions 36. Solve for x: 10 x − 2(3 − x ) = −3(4 + 2 x ) − 2x 37. Solve for x: 8 ( 14 x − 12 ) = −2(2 − 14 x ) 38. 9x 39. Graph the line whose equation is given by y = 2x + 3 . 40. Graph the line whose equation is given by x − 3 y = 12 . 41. Graph the line whose equation is given by − 53 x − 13 y = −2 . qxd 4/24/12 11:07 AM Page 31 501 Calculus Questions 42.

Observe that this holds when c = 3 and d = 1 . Hence, we conclude that 4u 2 + 8u + 3 = (2u + 3)(2u + 1) Now, resubstitute u = x −4 into the factored expression to obtain 4 x −8 + 8 x −4 + 3 = ( 2 x −4 + 3)( 2 x −4 + 1) Neither of the two binomials on the right side factors further over the set of real numbers. 19. qxd 4/25/12 12:39 PM Page 21 501 Calculus Questions 20. First, rewrite the expression underneath the radical sign as a product of terms raised to the fourth power and terms whose powers are less than 4 to obtain 4 3 4 3 −1 4 −2 3 4 3 4 32w 3 x 7 y −6 z 15 = 4 2 ⋅ 2w x x ( y ) y ( z ) z = = 4 ( 2xy ) −1 3 4 z ⋅ 2w 3 x 3 y −2 z 3 Now, simplify the radical expression using the fact that obtain the simplified expression a 4 = a to z ) ⋅ 2w 3 x 3 y −2 z 3 = ( 2xy −1 z 3 ) 4 2w 3 x 3 y −2 z 3 21.

Undefined 76. ( f ( f ( f ( f (5))))) = ______________ . a. b. c. d. 0 –1 3 undefined 77. True or false? The real number 0 belongs to the domain of the function h defined by h(x ) = ( g g )( x ) . qxd 4/25/12 12:42 PM Page 45 501 Calculus Questions 78. Which of the following is the domain of the function f ( x) = 1 2 ? (2 − x ) 5 a. ( −∞, 2 ) b. ( 2, ∞ ) c. ( −∞, 2) ∪ ( 2, ∞ ) d. none of the above 79. True or false? There are two x-intercepts of the function f (x ) = 1 − 2 x − 1 . 80. Determine the inverse function for f ( x) = x −1 5x + 2 , x ≠ − 52 .