501 Calculus Questions by Mark McKibben

By Mark McKibben

Designed for these looking aid learning calculus in class - additionally helpful for adults trying to learn/re-learn calculus. A source for teachers supplementing their guideline. 501 Calculus difficulties is helping clients organize for educational tests and construct problem-solving abilities. not like textbooks, complete solution factors are supplied for all difficulties. comprises: - Questions protecting all of unmarried variable calculus - universal calculus blunders - precise answers/fully labored recommendations - word list and theorem record - entry to loose on-line try

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Qxd 4/25/12 12:39 PM Page 22 501 Calculus Questions 23. Since the radical term is already isolated, we begin by squaring both sides, and subsequently moving all terms to the left side (so that the coefficient of the term with the largest exponent is positive). z = z + 12 z 2 = z + 12 z 2 − z − 12 = 0 Now, factor the expression on the left using the trinomial method to obtain the equivalent equation ( z − 4)(z + 3) = 0 Since the product of two real numbers is zero if and only if one of the numbers itself is zero, we conclude that at least one of ( z − 4) and (z + 3) is zero, so that the solutions of the factored equation are z = −3 and z = 4 .

Using the fact that a = b if and only if a = ±b , we solve the two equations 2x − 1 = ±1 separately, as follows: 2 x − 1 = −1 2x − 1 = 1 2x = 0 2x = 2 x=0 x =1 Thus, there are two x-intercepts of the given function. 80. Determining the inverse function for f requires that we solve for x in the expression y = 5xx −+12 , as follows: y = 5xx −+12 y(5 x + 2) = x − 1 5 xy + 2 y = x − 1 5xy – x = –2y – 1 x(5 y − 1) = −2 y − 1 x= −2 y − 1 5y −1 Now, we conclude that the function f −1 ( y) = −2 y − 1 , y ≠ 15 is the inverse 5y −1 function of f.

Which of the following is true of f(x) = a. The domain of the function is all real numbers greater than 14 , and the range is all real numbers greater than 0. b. The domain of the function is all real numbers greater than or equal to 14 , and the range is all real numbers greater than 0. c. The domain of the function is all real numbers greater than or equal to 14 , and the range is all real numbers greater than or equal to 0. d. The domain of the function is all real numbers greater than 0, and the range is all real numbers greater than or equal to 14 .

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