Application of derivatives Questions and Answers

Solve the following equation for x Give your answer as a fraction 3 In 81 In 5 3 In 8 4 X In x

mplify the following a 82 logg 6 b log7 1 4 74

Solve the given equation for x Round your answer to four decimal places 9 1 053x 1 3x 1 15 X

Od 1973 Graph the function x 1 1 a b 12 12 84 Select one OA a OB b OC C OD d 8 4 7 8 12 12 G 8 4 8 4 1793 8 12 4 4 8 12 x 12 x C d 12 8 12 8 12 12 8 12 V 4 4 8 F 12 x

8 Substitutes complements or unrelated You work for a marketing firm that has just landed a contract with Run o raskels and cannies All of these products have been on the market for s advertisement that will market two of the products that consumers will li complements are typically consumed together while substitutes can take Run of the Mills provides your marketing firm with the following data W sold decreases by 7 and the quantity of cannies sold increases by 7 other goods to determine which goods your marketing firm should adver

What is the length of the major axis of the ellipse x 3 y 2 12 17 7 3

Sketch the region enclosed by x y 56 and x y 0 a Favoring convenience should you integrate with respect to or X Y b What are the limits of integration lower limit and upper limit c Find the area of the region by integrating

If x 3 is a factor of x 2x kx then A x 1 K

If sec 0 0 and tan 0 then in which quadrant does 0 lic D or III B il E IV C III

Find the reference angle for the given angle a b c 9n 10 9n 8 10 3

Find the reference angle for the given angle a b c 130 190 285

3 A rectangular box with a volume of 125 cubic inches has a square base Find a function that models its surface area S in terms of the length z of one side of its base 4 A farmer has 2400ft of fencing and wants to fence off a rectangular field that borders a straight river He does not need a fence along the river s edge What are the dimensions of the field of the largest land area that he can fence off Hint Model the problem in one of two ways either using the length and or using the width Then find the maximum value of the function Use that to determine the field s dimensions length and width

You and your team are now want to build a transition area between the Theme Park and the Rio Grande Zoo It will have covered walkways gardens restrooms a refreshment station and a playground for kids Below is a grid of the area with an already established paved path marked that you plan to keep The established path is represented by a red line Use the graph provided on the last page to complete the following instructions 1 What is the equation of the red line representing the established path Label the red line on the graph path A 1 points 2 There needs to be a path parallel to the red path path A that goes through point 0 12 Find the equation that will represent this path graph the equation and label it path B on the graph 3 points 3a The third path needs to be perpendicular to Path A B and goes through point 6 10 Determine the equation of the line graph the equation and label it Path C 3 points b Write down the equations for Path A and Path C as a system of equations then look

AT1800 Business Statistics SP1 2023 Test Final Exam Study Guide uestion list Question 1 Question 2 K You are testing the null hypothesis that there is no linea a What is the value of tSTAT b At the x 0 05 level of significance what are the crit c Based on your answers to a and b what statistica d Construct a 95 confidence interval estimate of the OA Ho B 0 H B Q

e the slope and y intercept to graph the function f x 2x 4

2 1 c cos 0 cos 0 single trigonometric can be written in a identity as

2 1 cos 0 tan 0 2 can be simplified as

Draw a Venn diagram to illustrate the statement If you are the treasurer of your club then you are a sophomo

Use the given partitions to compute the products in Exer cises 15 and 16 Check your work by computing the same products without using a partition Show all your work 15 1 0 0 01 1 2 0

06 03 HC Let sine 3 2 and x 5 Part A Determine the exact value of cos 20 Part B Determine the exact value of sin X 5 1 C O

For the function y f x 4x 6 df dx a Find at x 8 f 8 b Find a formula for x f y f y df dy f f 8 c Find at y f 8

2 20 Pts a Find the Fourier coefficients ao and an of the delta function So 8 t 0 t 0 0 t 0 defined between to b In class we also defined the delta function as a sum of sinusoids of all frequencies Using the values you found in a write the Fourier series of the delta function to show this is true c Make a plot of your Fourier series for t and 1 n 10 to illustrate how this partial sum approximates 8 t What is the height of the spike at t 0

Find the following using the table below 3 4 3 4 2 4 3 2 1 X 1 2 f x 1 2 f x 4 1 3 g x g x 4 3 2 1 h 2 if h x f x g x f x g x h 2 if h x f g x h 2 if h x

Find f g f g fg and f g and their domains f x 2 x g x x 9 Find f g x 7 Find the domain of f g x Enter your answer using interval notation 0 00 Find f g x 2x 7 X Find the domain of f g x Enter your answer using interval notation 0 00 Find fg x x 11x 18 Find the domain of fg x Enter your answer using interval notation 0 00 Find 4 x x 2 x 2 x 3 x 3 X

Find f g x 6x 2x 1 Find the domain of f g x Enter your answer using interval notation 00 00 Find f g x 4x 2x 1 Find the domain of f g x Enter your answer using interval notation 0 00 Find fg x 25x 1 Find the domain of fg x Enter your answer using interval notation 0 00 Find X 4 x x 2x 5x2 1 Find the domain of x Enter your answer using intonal no

Find the derivative of 6 sin 2x Hint sin x sin x so use the chain rule twice

MATH 140 Online W X A ALEKS Charles Fiddler Learn https www awu aleks com alekscgi x Isl exe 1c NOMIAL AND RATIONAL FUNCTIONS ing a rational function with more than one vertical tional function x 8x 16 x 6x wing the vertical and horizontal asymptotes Then p on the graph a function button

Let f x 4x 4x 2 f x f 3

x x 2 simplified y x 1 y x x 2

The figure shows the graph of y ax bx c Suppose that the points h yo 0 and h y are on the graph The area enclosed by the 2 parabola the x axis and the lines x h and x h may be given by the formula below Find the area enclosed by f x x 4x 8 the x axis and he lines x 4 and x 4 Area The area is h 3 Y0 4y y2 Type an integer or a fraction h yo h Y 0

f x x 8 g x x Find fog x x 8 Find the domain of fog x Enter your answer using interval notation 0 00 Find gof x Find the domain of gof x Enter your answer using interval notation Find fof x X Find the domain of fof x Enter your answer using interval notation

Consider the following functions f x x 8 g x x Find fog x x 8 Find the domain of fog x Enter your answer using interval notation 0 00 Find gof x 3 x 8 Find the domain of gof x Enter your answer using interval notation 0 00 Find f of x 1 Find the domain of f of x Enter your answer using interval notation

graph the piece wise functions please Make sure to include if the functions have an open dot or a closed dot for ar immediate upvote thank you Sketch a graph of f x 5 4 3 2 1 Clear All 5 4 3 2 1 2 1 2 3 4 5 Draw Line if x 1 x 1 if 1 x 1 if x 1 1 2 3 4 5 est Dot Open Dat

Find fog x x 8 Find the domain of fog x Enter your answer using interval notation 0 00 Find gof x Find the domain of gof x Enter your answer using interval notation Find fof x Find the domain of f of x Enter your answer using interval notation Find go g x Find the domain of g o g x Enter your answer using interval notation

Find the quadratic Taylor polynomial about 0 0 for the function 9x y f x y Q x y e 1 9x 2y 40 5 x y X

40m2n m n 2mn2 10m n Use integers or fractions for any numbers in the expression Use positive exponents

12y 16y 8 4y Simplify your answer

4k k7 2 3k 2 Simplify your answer Type an integer or an improper fraction

Find f g x 2x x f x x x Find the domain of f g x Enter your answer using interval notation 0 00 Find f g x X Find the domain of f g x Enter your answer using interval notation 0 00 Find fg x x x g x x Find the domain of fg x Enter your answer using interval notation 0 00 Find x 1 1 Find the domain of 4 x Enter your answer using interval notation

Find f g f g fg and f g and their domains f x 2x g x x 9 Find f g x 2x 11 Find the domain of f g x Enter your answer using interval notation 0 00 Find f g x 7 Find the domain of f g x Enter your answer using interval notation 0 00 Find fg x X Find the domain of fg x Enter your answer using interval notation 0 00 Find 4 x F

Consider the following functions f x x 2x g x 5x 1 Find f g x Find the domain of f g x Enter your answer using interval notation Find f g x Find the domain of f g x Enter your answer using interval notation Find fg x Find the domain of fg x Enter your answer using interval notation Find 4 x Find th f ex

Find f g f g fg and f g and their domains f x 4 x g x x 3x Find f g x Find the domain of f g x Enter your answer using interval notation Find f g x Find the domain of f g x Enter your answer using interval notation Find fg x Find the domain of fg x Enter your answer using interval notation Find Find the domain of f x Enter your answer using interval notation

Minimize z 4x 3y 4y 5x 2y x 2 Subject to 2y 2x x Minimum is I 1111 y ALALAI AI AI R 32 8 14 0 0 at

Which values are in the domain of the given circular function s in radians a 5 in the domain of sin s b TT c 1 T d 0 2 e 11 5 in the domain of cot s in the domain of tan s in the domain of csc s in the domain of sec s

What is the solution to the equation below log20x 2log x 4 O X 25 O X 50 O X 250 Ox 500

What is the range of the function y e4x Oy 0 O y 0 O y 4 O y 4

Calvin deposits 400 in a savings account that accrues 5 interest compounded monthly After c years Calvin has 658 80 Makayla deposits 300 in a different savings account that accrues 6 interest compounded quarterly After m years Makayla has 613 04 What is the approximate difference in the number of years that Calvin and Makayla have their money invested O Makayla invests her money 1 year longer Makayla invests her money 2 years longer O Calvin invests his money 1 year longer O Calvin invests his money 2 years longer

below Year 1970 1980 1990 2000 2010 College Enrollment Percentages for Females 25 5 30 3 38 3 45 6 50 5 Let a represent time in years since 1970 and let y represent the corresponding percentage of female high school graduates who enrolled in college See the Regression page in the Getting Started module for details on creating a regression model Find the cubic regression model Question 5 y F x ax bx cz d where a is rounded to 6 decimal places bis rounded to 4 decimal places cis rounded to 3 decimal places and dis rounded to 1 decimal place Use this cubic regression model to answer questions 5 6 below Use the cubic regression model above to answer this question 2 pts

3 Suppose you begin your career on your 23rd birthday You start a retirement account in which you deposit 200 dollars every month until you retire on your 55th birthday Upon your retirement you begin making monthly withdrawals from this retirement account If you want the retirement fund to last until your 90th birthday determine the size of the largest withdrawal that can be made from the account each month during your retirement Assume the retirement account earns 7 5 interest compounded monthly

Let Use logarithmic derivative f x x x6x differentiation to determine the