By Mark McKibben

Designed for these looking aid learning calculus at school - additionally precious for adults trying to learn/re-learn calculus. A source for teachers supplementing their guide. 501 Calculus difficulties is helping clients organize for educational tests and construct problem-solving talents. in contrast to textbooks, complete solution causes are supplied for all difficulties. contains: - Questions protecting all of unmarried variable calculus - universal calculus error - particular answers/fully labored ideas - word list and theorem record - entry to unfastened on-line attempt

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**Example text**

Since the x term is squared, the smallest value that this term can equal is 0 (when x = 0). Therefore, the smallest value that f(x) can attain occurs when x = 0. Observe that f(0) = 02 – 4 = –4. Therefore, the range of f(x) is the set of all real numbers greater than or equal to –4. 69. a. Any real number can be substituted for x, so the domain of the function is the set of all real numbers. The range of a function is the set of all possible outputs of the function. Since the x term is squared, then made negative, the largest value that this term can equal is 0 (when x = 0).

Isolate the radical term on one side of the equation by dividing by 3, then square both sides to obtain 3 x = 18 4 ( 2xy 4 −1 3 4 x =6 x = 36 22. 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 .

The equation x − 3 y = 12 written in slope-intercept form is y = 1 x − 4 . 3 The slope of the line is 13 and the y-intercept is –4. Hence, the graph of the line x − 3 y = 12 is given by y 7 6 5 4 3 2 1 x –5 –4 –3 –2 –1 1 2 3 4 5 6 7 8 9 –1 –2 –3 –4 –5 –6 41. The equation − 5 x − 1 y = −2 written in slope-intercept form is 3 3 y = −5 x + 6 . The slope of the line is –5 and the y-intercept is 6. Hence, the graph of the line − 5 x − 1 y = −2 is given by 3 14 3 y 12 10 8 6 4 2 –8 –6 –4 –2 2 4 6 8 10 12 14 x –2 –4 –6 –8 –10 –12 –14 42.