Math 1190 Exam 1 Review PDF

Exam 1 review for Math 1190. The exam will tentatively cover 1.0 Intro, Rational Inequalities, and Sign Charts 1.1 Idea of a Limit and Limit Rules 1.2 Limit Rules 1.3 Continuity 1.4 Limits at Infinity and Infinite limits 1.5 Average Rate of Change and Tangent Lines by Graphing 1.6 Defi...

Exam 1 review for Math 1190. The exam will tentatively cover 1.0 Intro, Rational Inequalities, and Sign Charts 1.1 Idea of a Limit and Limit Rules 1.2 Limit Rules 1.3 Continuity 1.4 Limits at Infinity and Infinite limits 1.5 Average Rate of Change and Tangent Lines by Graphing 1.6 Definition of the Derivative The review is broken up into 3 sample exams. For best results: 1. Take the first sample exam with no notes in a setting similar to your classroom environment. 2. Grade yourself with the attached key. Review the problems you missed, review related material in your notes and get questions you still have answered. 3. Take the next sample exam(s) and then repeat steps 1 and 2. Repeatedly reviewing this material will go a long way toward helping you understand the material. Of note, some problems may be of a different form on the exam to make them more appropriate for time considerations or to adapt them to a multiple choice format. Be sure to focus on learning and understanding when going through the review, not just memorizing how to do these problems. The length of this review is not intended to be a good gauge as to the length of the exam. You will have the normal class time for the exam and I will write the exam with that in mind. Also, this review is not intended to cover absolutely everything possible that may be on the exam. Be sure to also review your notes and your homework notebook. * - A key is attached, but there may be errors. If you see a problem, please ask! 1 Sample Exam A: 1. A rational inequality of the form R(x) ≥ 0 gives the following number line: R(x) +++ U nd. − − − U nd. + + + 0 −−− x −2 1 4 Solve the inequality. Your answer should be in interval notation. 2. What must be true between for the value of a function any two partition numbers? 3. Use the table below to answer the questions that follow: x f (x) x f (x) 3 6 5 11 3.9 7.92 4.1 9.07 3.99 7.99992 4.01 9.00007 3.9999 7.99999999992 4.00001 9.00000000007 Write, with limit notation, what this table seems to indicate about f (x) about with respect to limits. 4. Use the graph of f (x) below to answer the questions that follow. 6 y 5 4 3 2 1 y = f (x) −2 −1 1 2 3 4 5 x6 −1 −2 A) Find lim f (x) x→2 B) Find f (2). C) Find lim f (x) x→1 D) Find f (1) x2 + 3x − 4 5. Evaluate lim x→−1 x2 − 16 √ 6. Find lim 6x − 4 x→5 x − g(x) 7. If lim f (x)= −3 and lim g(x)= 7, find lim. x→2 x→2 x→2 f (x) 2  8. What is required for a function f (x) to be continuous at x = a? 9. Where is the function f (x) below discontinuous?  4,  if x < −3 2 f (x) = x − 5, if − 3 ≤ x ≤ 1  x + 3, if x > 1  10. Find a value for k so that f (x) is continuous if ( 2 + kx x ≤ 1 f (x) = 5 + 3x x > 1 x(x2 − 9) 11. Find the x-values of the holes and vertical asymptotes of R(x) =. (x + 1)(x − 3)(x + 5) −7x −7x 12. Find lim 2. What does this tell you about the graph of y = 2 ? x→−∞ x + 1 x +1 13. Find the average rate of change of f (x) = 6x2 − 2x + 7 from x = 1 to x = 5. 14. Find and simplify the average rate of change of g(x) = x2 − 4x from x = 1 to x = t. 15. On the graph below, which point would have a tangent line with slope closest to m = 2? 11 y 10 C 9 8 7 B D 6 5 4 3 y = f (x) 2 1 A E x −1 −1 1 2 3 4 5 6 7 8 9 10 16. State the definition of the derivative. 17. Use the definition of the derivative (i.e. the four step process) to find the derivative of f (x) = 7 − 4x2. 18. What are the two primary interpretations of the derivative? 3  Use the graph of y = f (x) below to answer questions 19-22. 10 y 9 (4, 9) 8 7 6 5 4 3 2 1 y = f (x) x −1 1 2 3 4 5 6 7 8 9 10 −1 19. Find the slope of the secant line from x = 3 to x = 6. 20. Find the average rate of change from x = 4 to x = 5. 21. What is the derivative of y = f (x) when x = 3? Note the dashed line on the graph is the tangent line at x = 3. 22. Where is the tangent line to y = f (x) horizontal? 4 Sample Exam B: x(x + 4) 101. Solve the inequality ≥ 0. (x − 2)2 102. Use the table below to answer the questions that follow: x f (x) x f (x) 3 6 5 11 3.9 7.92 4.1 9.07 3.99 7.99992 4.01 9.00007 3.9999 7.99999999992 4.00001 9.00000000007 Draw a graph in based on the table above in which f (4) = 9. 103. Use the graph of f (x) below to answer the questions that follow. y A) f (3) = 6 5 B) lim f (x)= x→3− 4 3 C) lim f (x)= x→3+ 2 D) lim f (x)= 1 y = f (x) x→3 x −2 −1 1 2 3 4 5 6 7 8 E) f (4) = −1 −2 F) lim f (x)= x→4− −3 G) lim f (x)= x→4+ −4 −5 H) lim f (x)= x→4 104. If lim f (x)= 4 and lim g(x)= −5, find lim 2f (x) + g(x). x→−1 x→−1 x→−1 105. Find lim f (x) if x→1+  2 x −1   x>1 f (x) = x2 + 1 x − 1  x1 f (x) = x2 + 1 x − 1  x