By Mark McKibben
Designed for these looking aid learning calculus at school - additionally helpful 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 abilities. not like textbooks, complete solution motives are supplied for all difficulties. contains: - Questions protecting all of unmarried variable calculus - universal calculus error - unique answers/fully labored recommendations - word list and theorem record - entry to loose on-line try out
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The arrowheads on the ends of the curve imply that the graph extends upward, without bound, as x tends toward both positive and negative infinity. Hence, this line touches the graph of f(x) in two places. Therefore, there are two values for which f(x) = 10. b. Begin with the innermost function: find f(–2) by substituting –2 for x in the function f(x): f(–2) = 3(–2) + 2 = –6 + 2 = –4 Then, substitute that result in for x in g(x). g(–4) = 2(–4) – 3 = –8 – 3 = –11 Thus, g( f(–2)) = –11 d. Begin with the innermost function: find f(3) by substituting 3 in for x in the function f(x): f(3) = 2(3) + 1 = 6 + 1 = 7 Next, substitute that result in for x in g(x).
X − 2 c. 83. If f ( x) = −3x and g (x ) = 2x 2 + 18 , then the domain of g f is ____________. a. [ 0, ∞ ) b. ( −∞,0 ] c. ޒ d. none of the above 84. If f (x ) = 1 , simplify 2x the expression f ( x + h) − f ( x ) , where h h ≠ 0. 85. Which of the following sequence of shifts would you perform in order to obtain the graph of f ( x) = ( x + 2)3 − – 3 from the graph of g (x ) = x 3 ? a. Shift the graph of g(x) up three units and then left two units. b. Shift the graph of g(x) down three units and then right two units.
Y = 3x − 1 d. y = 13 x + 1 43. Which of the following linear equations has a negative slope? a. b. c. d. y = 3x − 5 −1 = y − x −2 x + y = 3 6 y + 2x = 5 44. Find the equation of the line whose graph contains the points ( −2, −4 ) and ( −6,5) . 45. Solve for x: 3x + 5 = 8 46. How many different values of x satisfy the equation 2 x + 1 = 4 x − 5 ? a. b. c. d. qxd 4/24/12 11:07 AM Page 32 501 Calculus Questions For Questions 47 through 50, solve the inequality. Express the solution set using interval notation.
501 Calculus Questions by Mark McKibben