2. Find the value of y for which the line through A and B has the given slope m: A(-2, 3), B(4, y), 2 3
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1 . Find an equation for the line that contains the points (, -) and (6, 9).. Find the value of y for which the line through A and B has the given slope m: A(-, ), B(4, y), m.. Find an equation for the line that contains the coordinate (, ) and is perpendicular to the line 6 y. 4. For what value of k are the two lines ky and y a) Parallel? b) Perpendicular? For questions -0, let f ( ) and g ( ).. ( f g)( ) 6. ( g f )(6) 7. g ( ) 8. ( g f )( ) 9. f ( ) 0. ( f g)(). Algebraically find the inverse of y.. If f ( ), find f and verify that f ( f ( )) f ( f ( )). For questions -0, simplify each epression completely.. 4. ln e. ln 6 7 ln e 7. log 8 8. e ln
2 9. 4y y Rewrite ln( ) ln( ) 6ln as a single logarithmic epression. t. Solve for t: (.04). Solve for : log log ( 4) 4. Solve for : 7 9. Solve for : ln( ) 6 6. Evaluate log to the nearest thousandth The number of elk after t years in a state park is modeled by the function P( t) 0. 0t 7e a) What was the initial population of elk? b) When will the number of elk be 70? c) What is the maimum number of elk possible in the park? 8. Arturo invests $700 in a savings account that pays 9% interest, compounded quarterly. If there are no other transactions, when will his balance reach $40? 9. Without using a calculator, find the eact value of cos 7 cos. Justify your answer.
3 For questions 0-, find the eact values of each trigonometric function sin. 6 csc 60. cos 0. sec 4. tan. cot( ) 6. Simplify (csc( ) tan( ))sin( )cos( ) 7. List the three Pythagorean Identities. 8. List the double angle formulas a) sin = b) cos = 9. List the sum and difference formulas. a) cos( ) b) sin( ) sin cos 40. Prove that csc cos sin 4. Prove that (sin cos ) sin 4 4. Determine the range of f ( ) 0. Also, find the maimum and minimum values of f(), and state where those values occur.
4 4. Find the equation for the parabola whose verte is (, -) and passes through (4, 7). Epress your answer in standard form for a quadratic. 44. Consider the circle of the radius centered at (0, 0). Find an equation of the line tangent to the circle at the point (, 4) in slope-intercept form. 4. Determine all points of intersection for y 4 and y. 46. Find the points of intersection in the graphs of y and y Use a graphing calculator to approimate all of the function s real zeros. Round your results to 6 decimal places. f ( ) Algebraically determine whether the function is even, odd, or neither: y 49. Determine whether the function is even, odd, or neither: f ( ) sin 0. Graph the piecewise function on the attached graph paper. f ( ) For the function below, give the zeros (if non eist, write none), domain, range, VA s, HA s, and/or points of discontinuity (holes-as ordered pairs)if any eist. Also sketch the function s graph. f ( )
5 For questions -, graph each function on the attached graph paper. Give its domain and range.. y e. y = 4. y sin. y 6. Einate the parameter and write a rectangular equation for y t t 7. Epand and simplify. a) 4 n 0 n b) n n 8. Find the 9. Find the ( 4) 60. Find the 6. Find the Find the ln( ) 6. Find the t 6t t ( t)(t ) 64. Find the cos 6. Find the sin Find the Find the
6 68. Find the f ( ), where f ( ),, 69. Find the slope of the tangent line to the graph of g ( ) 4 at the point (, -). 70. Find an equation of the tangent line to the hyperbola y at the point (, ). 7. Find an equation of the tangent line to the graph of f ( ) 8 9 a the point (,-6). For questions 7-74, find the -values (if any) at which f is not continuous. Which of the discontinuities are removable. 7. ( ) 7. f ( ) cos f 74. f ( ) 0 For questions 7-94, find the derivative of each given function. 7. f ( ) 76. f ( ). 77. y e 78. f ( ) g ( ) f ( ) 4
7 8. f ( ) e 8. f ( ) e 8. f ( ) 84. tan (8 ) 8. y sin cos 86. y cos 87. f ( ) cos tan 88. f ( ) cot sec g ( ) ( ) 90. y y ( ) ( ) 9. y ln( ) 9. Find y of y log If f ( ) e, find the value of f '() 9. If f ( ), find ( ), f ( ), f and f () dy For questions 96-97, find by implicit differentiation. d 96. y 97. y y 8
8 98. If a billiard ball is dropped from a height of 00 feet, its height s at time t is given by the position function: s 6t 00 where s is measured in feet and t is measured in seconds. Find the average velocity of each the following time intervals. a) [, ] b) [,.] c) [,.] 99. Suppose that a ball is dropped from the upper observation deck of the CN Tower, 40 m above the ground. a) What is the velocity of the ball after seconds? b) How fast is the ball traveling when it hits the ground? 00. A particle moves according to a law of motion s f ( t) t t 6t measured in seconds and s in meters. a) Find the velocity at time t. b) What is the velocity after s? c) When is the particle at rest? d) Find the total distance traveled during the first 8 s. e) Find the acceleration at time t. f) Find the acceleration after s., t 0, where t is
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