Application of derivatives Questions and Answers

By the Integral Test 8 the infinite series 6ne n OA converges B diverges lhe whether the infinite series is convergent n 3 8 Fill in the corresponding integrand and the value of the improper integral Enter inf for co inf for o and DNE if the limit does not exist Compare with 36xe x 2 n 3 6ne n dx

The following series are geometric series or a sum of two geometric series Determine whether each series converges or not For the series which converge enter the sum of the series For the series which diverges enter DIV without quotes a b c M8 M8 M8 M8 M8 M8 d e 1 7 6 1 2 DIV 6 7 2 42n 1 9 9 4 11 DIV 6 2 7

Determine the values of x for which the function as represented by the graph to the right is continuous If the function is not continuous determine the reason Select the correct choice below and if necessary fill in the answer box to complete your choice OA The function is not continuous at x because a small change from this value of x may produce a large change in f x Use a comma to separate answers as needed OB The function is continuous for all values of x The function exists for all points and any small change in x produces only a small change in f x because the function does not exist there OC The function is not continuous at x Use a comma to separate answers as needed

1615 14 13 12 11 10 8 7 6 5 4 3 2 so f x 1 2 3 0 78 9 10 11 12 The curve above is the graph of a sinusoidal function It goes through the points 12 2 and 2 2 Find a sinusoidal function that matches the given graph If needed you can enter 3 1416 as pi in your answer otherwise use at least 3 decimal digits

For the right triangle below find the measure of the angle Figure is not to scale 8 Q

Northland Calc own deep enough in

Question 4 10 points Identify the end behavior of the polynomial function g x x 3 Hint It may help to graph the polynomial function with your calculator first O As the graph of the polynomial continues to the left the graph moves upward As the graph of the polynomial continues to the right the graph moves upward O As the graph of the polynomial continues to the left the graph moves upward As the graph of the polynomial continues to the right the graph moves downward O As the graph of the polynomial continues to the left the graph moves downward As the graph of the polynomial continues to the right the graph moves upward O As the graph of the polynomial continues to the left the graph moves downward As the graph of the polynomial continues to the right the graph moves downward

K Determine a the area and b the perimeter of the qua

Determine a the volume and b the surface area of figure Use the button on your calculator

K Watch the video and then answer Click here to watch the video The following figures are similar A A F 36 B 16 20

Determine the measure of an If a side of the polygon is exte Nonagon The measure of each interior The moocure of the suppleme

30 Use this information to find the unknown parts of the triangle a 32 B 32 C 71 b A 33 B 59 O C 31 D 17

44 Given b 4 1 c 6 2 A 114 what is the area a 10 3 b 23 2 c 5 2 d 11 6

C a b C d 32 sin 32 sin 77 32 sin 71 sin 77 32 sin 77 sin 71 32 sin 77 sin 32

26 Find the antilogarithm 7 3139 10 a 00206 b 0000206 c 000206 d 0206

27 Find the antilogarithm 2 9 a 85 64 b 85 66 c 856 4 d 856 6

12 Given a graph of the derivative a State on what interval original gra b Inflection points of original graph c Intervals of Concavity x

K Triangles ABC and DEC in the figu Determine the length of side BC

Express the number as a ratio of integers 3 157 3 157157157

Let an 40 7n 1 a Determine whether a is convergent O convergent Odivergent an b Determine whether convergent divergent n 1 is convergent

Given z 2 i 1 i a 2i 3 i find the value of a such that a E R and Rez Imz

Given that a bi 2i 1 i Find the value of a b where a b E R

that Z 3i 7 and z2 Z 10i 4 Find where is the angle in radians between z and 22

Find the centroid of the region bounded by the given curves y x 5 x y 2 and x 0 O 0 4 5 O None of the answer choices O 28 75 92 105 1 2 37 5

The function f x P q r e Z 2x 1 1 x 3 x is equivalent to the function h x 1 3 x whe Determine the values of p q and r writing your answer in the form p q r

5 log 0 x 3 log 0 X 1 x a 2 5 b 5 2 c 5 d 2

19 Write the expression 3 log x logy log z as a single a log x z2 y4 b log y z 4 2 3x 3x c log d log y 4 Z 2 x3 11 y4z2

8 logx a b C d 9 4 81 16 MINN 16 81 2 X

6 log3 x 5 x a 125 b 243 c 625 d 81

Find the derivative of S 5v dv O 5x O None of the answer choices O 5x 5 O 5x sqrt x

6 km d 8 200 8 6 0 20 8 0 20 8 36 20 8 208 36 400 3007 64 100 2 360 400

Use the figure to the right to a identify th markings the two small parallel lines on

Use the fundamental identities and the given information to find the exact values of the remaining trigonometric functions of 3 5 tan x and secx 4 3 O A sinx cos x 5 O B sinx Q c sinx 35 D sinx 5 4 5 1 2 5 I COS X COS X 4 1x COS X 5 4 5 5 3 5 3 5 CSC X CSC X CSC X CSC X 5013 3 5 3 5 3 5 3 cotx cot x cot x cotx 4 11 13 I 1 4 3 43

a The cost at the production level 1600 b The average cost at the production level 1600 c The marginal cost at the production level 1600 d The production level that will minimize the average cost e The minimal average cost Question Help Video Submit Question Question 3 Jump to Answer For the given cost function C x 72900 600x x First find the average cost function Use it to find a The production level that will minimize the average cost x b The minimal average cost 0 1 pt10099

A fence 24 feet tall runs parallel to a tall building at a distance of 6 ft from the building as shown in the diagram 0 LADDER 24 ft 6 ft Q We wish to find the length of the shortest ladder that will reach from the ground over the fence to the wall of the building A First find a formula for the length of the ladder in terms of 0 Hint split the ladder into 2 parts Type theta for 0 L 0 B Now find the derivative L 0 Type theta for 0 L 0 C Once you find the value of that makes L 0 0 substitute that into your original function to find the length of the shortest ladder Give your answer accurate to 5 decimal places

Find the measure of angles 1 7 gi parallel and t is transversal m21 125 22 m 2

Question 16 6 5 4 3 2 y 3 2 1 Submit Question 4 1 2 3 4 Write an equation for the function graphed above Ad

15 14 13 12 11 10 9 8 7 6 5 4 3 2 1 1 The curve above is the graph of a sinusoidal function It goes through the points 13 0 and 1 0 Find a sinusoidal function that matches the given graph If needed you can enter T 3 1416 as pi in your answer otherwise use at least 3 decimal digits f x 7 8 9 10 11 12 13

Formative Assessment 7 Write the letter of the expression on the right that is equivalent to the expression on the left sin 20 cos20 sin20 COS csc8 2 cos 8 s 0 7 Unit 3 Topic 3 NO CALCULATOR 1 sin 0 1 sin 8 Name Date A cos 0 B sin 0 C cos 0 I cos D sin 0 E tan 20 H sec 20 F cot 20 G csc 20

Watch help video Given the following exponential function identify whether the change represents growth or decay and determine the percentage rate of increase or decrease y 760 1 325 Growth increase Submit Answer attempt 1 out of 2

Amplitude Period 8 7 Midline y 6 5 Based on the graph above determine the amplitude midline and period of the function 3 24

7 4 3x 1 1 9 2345 27 11 1 4x6 2 x3 10 I m lim 8118

5 6 Graphing Exponential Functions Complete the table of values rounded to two decimal places and sketch a graph of the function 5 X 2 1 0 5 0 0 5 1 2 f x 1 5e 6 X 3 2 14 1 0 1 2 3 f x 4e x 3

7 16 Graphing Exponential Functions Graph the function not by plotting points but by starting from the graph of y e Figure 1 State the domain range and asymptote 7 g x 2 ex 121778 h x e x 3

find average rate between 64000 and 79829

A student wishes to use a power series to approximate the value of the integral 2x cos x dx with at error of less than 0 001 Which of the following results would resemble that approximation A 0 8411 B 0 8413 C 0 8415 D 0 8417

1 Use integration by parts to evaluate the following indefinite integral fx5 ln 3x dx

f x y 2 4y 2 x 1 how to circulate both sides of the equation

5 y x y 1 I 2 III 2 YA X 2 X 6 y sin x sin y II IV YA X

0 1 Points Rewrite the expre 2 tan CSC x