Questions

Use implicit differentiation to find y dy da 2 123 y8 8x dy da fo

Suppose f x 1 5x4 d dx d dx f 8x f 4x8

lim sin x 2 sin 2 m

Find dy dx dy for y dx 8 X4 9x4 I 4x 9 x4 2x4 9 x 2 9 x4 2 X

Question Find the value of Se In a da by substitution and then partial fractions Round your answer to four dec In x x lnx 2x

Suppose f x 1 3x4 d dx f 6x d f 4x8 dx

Let f x 3x 3x 6 Use sqrt N to write VN f x

Suppose f 1 4 f 1 7 Find the following d da The value of x 3x 5x 3 at x 1 is

Use the following information f 6 2 f 6 2 Find the following d dx 4 x 2 x 2 at x 6 d dx 9 3g x 19 z at a g 6 4 g 6 3 at x 6

Let f x f x 1 4x 3x 8 5

Suppose f x and f x have the values shown 22 23 24 25 26 6 4 2 10 X f x 10 1 f x 9 9 6 0 Let g x f 3x 2x 16 g 4 Connot Ro Dotormingd

Suppose f x and f x have the values shown 4 5 6 X 7 8 f x 2 11 3 1 9 f x 1 6 6 9 7 Let g x f x 5 g 6 Cannot Be Determined

8 8 Let f x 4x 4x f x

Suppose f x 2x 6 and g x 3x 2 Find the following You do not need to simplify your answers The derivative of f x is f x 2 The derivative of g x is g x 3 The product of the derivatives is f x g x 6 2 The product of f x and g x is f x g x 6x The derivative of the product is f x g x 22x 12 OT O Q OT

Which of the statements a through k about the function y f x graphed here are true and which are false R 2 A X e The statement lim f x 1 is X 1 f The statement lim f x exists at every point c in X C 1 1 is g The statement lim f x does not exist is X 1 h The statement f 0 0 is i The statement f 0 2 is j The statement f 1 1 is k The statement f 1 2 is

The terminal side of 8 lies on the given line in the specified quadrant Find the exact values of the six trigonometric functions of 8 by finding a point on the line Quadrant II sin 8 cos e tan 8 csc 8 sec 8 cot 8 Line y x

Suppose f x 2x 6 and g x 3x 2 Find the following You do not need to simplify your answers The derivative of f x is f x 2 The derivative of g x is g x 3 The product of the derivatives is f x g x 6 The product of f x and g x is f x g x OT OT

Next question Suppose that x and y are both differentiable functions of t and are related by the given equation Use implicit differentiation with respect to t to determine dy dt x5 y5 2 4 5x 5y SCEN dy dt in terms of x y and dx dt

Suppose that x and y are related by the given equation and use implicit differentiation to determine x y 2 11 dy 11 dx x 3y 12y 12 11

The length of one side of a golden rectangle is 0 67 centimeters Find the length of the other side Notice that the other side could be either longer or shorter than the given side Use the approximation 1 62 for your work If 0 67 is the long side the short side is Round to two decimal places as needed If 0 67 is the short side the long side is Round to two decimal places as needed centimeters centimeters om quiz

Choose the best answer to the following question Explain your reasoning with one or more complete sentences Which line does the letter A have reflection symmetry along Choose the correct answer below OA It has reflection symmetry going diagonally through its middle The letter A remains unchanged when reflected across this line B It has reflection symmetry going diagonally through its middle A pattern composed of the letter A remains unchanged when translated in this direct OC It has reflection symmetry going horizontally through its middle A pattern composed of the letter A remains unchanged when translated in this direc OD It has reflection symmetry going vertically through its middle The letter A remains unchanged when rotated across this line OE It has reflection symmetry going vertically through its middle The letter A remains unchanged when reflected across this line OF It has reflection symmetry going horizontally through its middle The letter A remains unchanged when rotated across this line O

Given 1 2 inches is one side of a golden rectangle find the length of the other side Notice that the other side could be either longer or shorter than the given side Use the approximation 1 62 Round to two decimal places OA 3 14 in or 0 46 in OB 1 94 in or 0 74 in OC 3 14 in or 2 18 in D 1 94 in or 1 35 in

Given 6 6 kilometers is one side of a golden rectangle find the length of the other side Notice that the other side could be either longer or shorter than the given side Use the approximation 1 62 Round to two decimal places A 10 69 km or 4 07 km B 17 29 km or 2 52 km OC 10 69 km or 0 25 km OD 17 29 km or 0 40 km

Integrate a function by applying partial fractions after a substitution Question S Evaluate In a x In x ln x 6 Provide your answer below da by substitution and then partial fractions

Which of the following is the graph of r 12 12 cos 0 Note that the r grid lines occur in increments of 4 OA OB O C 0 OD Q 0 O E 0 0 OF 0 0 0 5

K Suppose you start with a golden rectangle and cut the largest possible square from one end of the rectangle What can be said of the remaining piece of the golden rectangle Choose the correct answer below OA The remaining piece of the golden rectangle is a logarithmic spiral because the remaining piece is an example of the Fibonacci sequence in nature B The remaining piece of the golden rectangle is a logarithmic spiral because the remaining piece is a smooth curve that can connect the corners of squares whose side lengths are proportional to p OC The remaining piece of the golden rectangle is another square because the side lengths of the remaining piece are all equivalent O D The remaining piece of the golden rectangle is another golden rectangle because the dimensions of the remaining piece still have a ratio of the longer side to the shorter side that is equal to 1 the OE The remaining piece of the golden rectangle is another square because the ratio of the original longer side to the original shorter side was 2 largest possible square is removed cut out from this 2 equivalent squares are created OF The remaining piece of the golden rectangle is another golden rectangle because the dimensions of the remaining piece still have a ratio of the longer side

Starting with a tone having a frequency of 181 cycles per second find the frequency of the tone that is four octaves higher OA 724 cps OB 1 448 cps OC 2 896 cps D 32 761 cps

erved offspring AABB 5 AaBB 15 aa88 8 see below Mating AaBb x AaBb 1 pt AABb 10 88bb 6 BaBb 30 aaBb 11 Babb 13 aabb 2 the observed offspring the result of the parents using chi square stati

Use a graphing calculator to find the approximate point of intersection of the pair of equations 2 1x 4 1y 11 4 y 1 1 In x 1 45 2 What is the approximate point of intersection Type an ordered pair Round to the nearest thousandth

A 2 1 3 and AB 3 4 be column 2 of B 3 1 6 1 8 9 determine the first and second columns of B Let b be column 1 of B and

Chlorophyll O is synonymous with bacteriochlorophyll is only found in bacteria O No answer is correct O is only found in plants

If h x T 3x 8x 5 3 5x find

If f t t 3t 4 6t 4 find t f t t

cos 0 7 cos 0 2 0 Solve in general

The complex bacterial media named Luria Bertani LB can be used to grow E coli and many other bacteria from the human gut But most microorganisms from the open ocean will not grow or will die on LB Why O They are anaerobes O They are autotrophs O They are oligotrophs

Given the following measurements which set will produce a single triangle OmZA 22 Om A 35 Om A 27 Om A 35 side a side a side a side a 17 cm side b 12 cm 12 2 cm side b 17 8 cm 33 cm side b 88 cm 11 cm side b 12 cm

If y dy da II 7x 8x 5 2x 6 find

5 Use the graph of y f x to answer the following a Determine 2 b Determine 3 I c Find all x for which f x 1 d Find all x for which f x 4 e Determine the x intercept s f Determine the y intercept g Determine the domain off h Determine the range of f 70

e 0 00012t A bone has lost 34 of its carbon 14 How old is the bone The amount of carbon 14 present in animal bones after t years is given by P t Poe The bone is years old Round to the nearest integer as needed

Emma is choosing a weekly meeting time She hopes to have two different managers attend on a regular basis The table shows the probabilities that the managers can attend on the days she is proposing Manager A Manager B Monday 0 82 0 88 Wednesday 0 87 0 85 Assuming that manager A s availability is independent of manager B s availability which day should Emma choose to maximize the probability that both managers will be available O A Monday The probability that both managers will be available is 0 72 OB Wednesday The probability that both managers will be available is 0 87 C Monday The probability that both managers will be available is 0 88 D Wednesday The probability that both managers will be available is 0 74

Suppose f 2 9z 2 Find f x in two ways First expand f x 81x 36x 4 f x 162x 36 You MUST base your derivative on the expanded form of f z Next since f x 9x 2 2 then f x 9x 2 9x 2 Find f x using the product rule DO NOT simplify f x You MUST base your derivative on the product rule DO NOT simplify OF

Find the indicated derivatives using the following information f 9 4 f 9 5 fg 9 9 9 g 9 9 g 9 5

Suppose f x 2x 6 and g x 3x 2 Find the following You do not need to simplify your answers The derivative of f x is x The derivative of g x is g x

Find the indicated derivatives using the following information f 9 4 9 5 If g x 8f x z6f z then g 9 If h x 5x 3 f x then h 9

AABC is a 30 60 90 triangle where two vertices are A 3 2 and B 3 2 AB is the hypotenuse and point C is in Quadran 1 Find the coordinates of point C

Most bacteria like to attach to surfaces So where do you expect to find them in sediments as biofilms on sand silt and clay particles O attached to air gas bubbles swimming in the pore water

Which of the following compounds would be used by a chemoorganotroph for generating energy O glucose carbon dioxide O light O iron

What is an average concentration of bacterial and archaeal cells in marine water at several thousand meters depth O 10 cells ml O 108 cells ml O 106 cells ml O 10 cells ml

2 The graph of the tilted ellipse 2 xy y 3 is shown below The sides of the box are vertical and horizontal and also are tangent to the ellipse a Find for the tilted ellipse dy dx b Find the points on the ellipse where the tangent line is horizontal c Find the points on the ellipse where the tangent line is vertical d What are the dimensions of the box containing the ellipse e What are the coordinates of the four corners of the box containing the ellipse

Which metric describes the number of different species present in a community O species diversity species abundance O species evenness O species richness