Limits & Continuity Questions and Answers

A farmer finds that if she plants 95 trees per acre each tree will yield 35 bushels of fruit She estimates that for each additional tree planted per acre the yield of each tree will decrease by 2 bushels How many trees should she plant per acre to maximize her harvest trees Give your answer rounded to the nearest whole number

X AX where A 5 3 3 1 x 0 1 2 text A None B B left begin array 1 1 3 2 3 end array right e 2 t quad x left begin array 1 1 2 2 t end array right e 2 D quad x left begin array 1 1 3 7 2 3 1 end array right e 2 t x left begin array 1 2 t 2 2 t end array right e 2

1 Find all solutions in the interval 0 2n 3 points cos x 2 cos x 1 0 Ox 2 OO Ox T O 7x x 4 4 3x T x 2 2

Let f x 4x 6x 1 What is the absolute minimum value of f over the closed interval 4 x 3 Choose 1 answer A B 78 3 353

If a rock is dropped from a height of 125 ft its poistion t seconds after it is dropped until it hits the ground is given by the function s t 16t 125 Round values below to 3 decimal places How long does it take the rock to hit the ground seconds Find the average velocity of the rock from when it is released until when it hits the ground feet per second What time after the rock is thrown will its instantaneous velocity be equal to its average velcity Apply the Mean Value Theorem seconds after it is thrown

Which function is graphed on the right O O y 2x 3 2 y 2x 3 2 y 2x 2 3 y 2x 3 RETRY 2 8 6 4 2 ty 2 X

Below is the graph of y b Find b b DONE 2 xt 2 Y St X

3 2 1 lowest middle 0 highest 12 For the above rational function f x 7 4 3 2 14 14 2 242 1 2 5 1 X 2 3 15x 3 5r2 1 identify its three inflection point

Second Derivative Test 1 Find the first derivative of the function g x 6x 45x 72z g x 2 Find the second derivative of the function g z 3 Evaluate g 1 g 1 4 Is the graph of g z concave up or concave down at x 1 At z 1 the graph of g z is concave 5 Does the graph of g z have a local minimum or local maximum at z 1 At z 1 there is a local

Consider the function f x 1 e 7 f x has two inflection points at x C and x D with CD where Cis and D is Finally for each of the following intervals tell whether f x is concave up type in CU or concave dov type in CD C C D D

Determine the zero s of s x x 7x 6x The zeros are x I

The workers union at a particular university is quite strong About 94 of all workers employed by the university belong to the workers union Recently the workers went on strike and now a local TV station plans to interview 5 workers chosen at random at the university to get their opinions on the strike What is the probability that exactly 2 of the workers interviewed are union members Round your response to at least three decimal places If necessary consult a list of formulas 0

20 1 point Graph each function f x 2 4 3 x 2 T 6 4 m da Tr 2 J 1 3 1 2 8 S M d T S 8 9 OF X

Textbook Videos Find the following using the table below H 1 2 3 4 f x 3 4 2 1 f z 14 2 g x g x 3 2 1 12 4 33 4 if h x f g x then h 1 Question Help Video

20 COS 57 2 21 sin 57 sin if cos a if cos a 31 18 17 8 assume cos 2 is negative a assume sin is positive 2

Given that f 1 r h 1 h 1 5 h 1 8 Calculate f 1 Use the product rule and the power

Textbook If f x 6x 4 4x 3 7 Submit Question find f x f 5 Question Help Video Videos Jump to Answer

Find the equation of the tangent line to the curve y 8 sin z at the point The equation of this tangent line can be written in the form y mz b where m and b

If f x 2x 6x 2 find f 3 Use this to find the equation of the tangent line to the parabola y 2x 6x 2 at the point 3 2 The equation of this tangent line can be written in the form y mz b where m is and where b is

Find the derivative of f z 2 2 Type your answer without fractional or negative exponents Use sqrt x for z f x Video 2 N

30 27 24 21 18 15 12 9 6 3 4 3 2 1 For the above function f x 4 0 6 estimate f z using h 0 001 for the following three values f 2 5 67 f 2 25 f 3 75

The limit below represents the derivative of some function f x at some number a 4 1 h 5 4 lim h 0 h State the function and the number f x a

1 q h q 493 1 1 1 2 1 3 1 4 460 429 400 400 373 Estimate h 1 2 using the table above h 1 2

Use the limit definition of the derivative to find the instantaneous rate of change of f x 7z 6x 6 at z 3

Let a and b represent real numbers Describe the possible solution sets of the linear equation ax b

Solve the y y tan x 1 provided differential equation 2 x 2

10 10 points Find the following SM cos 1 dt 1 a lim 0 x 17 00 e 1

aped below with the points A 21 56 B 0 14 C 14 22 a Identify the domain of f a b Identify the range of f x c Identify the relative minima of f z Your answer should be a list of ordered pairs d Identify the relative maxima of f a Your answer should be a list of ordered pairs Show Transcribed Text C O e Identify the absolute minimum of f z Your answer should be an ordered pair f Identify the absolute maximum of f x Your answer should be an ordered pair g Identify the interval on which f a is increasing

22 Given cos 8 and tan 8 0 find the sin e a 77 b 77 C 1 77 9 912 d 2

19 For what angles x in 0 2 does the sin x have the same value as cos cos 7 a b 7 5m 4 4 C d TC 5T 6 6 2T 3 4T 3 4T 5T 3 3

23 Find the coordinate point that corresponds with the point a 1 0 b 0 1 c 0 1 d 1 0

0 Evaluate tan a 1 9 V 24 b c 3 d 13 3 TC

1 tan 13 Simplify tan2x a 2 b csc x C secx d sin x

5 Find the amplitude and period of f x 5 cos x 2 5 Period 5 Period c Amplitude 5 Period 2 d Amplitude 5 Period 3 a Amplitude b Amplitude Swo

Rewrite each equation as requested a Rewrite as a logarithmic equation 1 57 25 b Rewrite as an exponential equation log 16 4 a log 0 0 b d 0 00 8

Evaluate the limit If the limit does not exist type DNE 3 8 lim 8 1 2 S

1 2 3 4 5 6 7 8 9 10 In Section 2 5 we learned the Chain Rule and how it can be applied to find the derivative of a composite function In particular if u is a differentiable function of x and fis a differentiable function of u x then d dx u x f u x u x In words we say that the derivative of a composite function c x f u x where f is considered the outer function and u the inner function is the derivative of the outer function evaluated at the inner function times the derivative of the inner function a For each of the following functions use the Chain Rule to find the function s derivative Be sure to label each derivative by name e g the derivative of g x should be labeled g x i g x e x ii h x sin 5x 1 iv g x 2 7x 4

15 In an examination of holiday spending known to be normally distributed of a sample of 16 holiday shoppers at a local mall an average of 54 was spent per hour of shopping Based on the current sample the standard deviation is equal to 21 Find a 90 confidence interval for the population mean level of spending per hour

Suppose that the functions g x 4x 1 r x 3x 4 Find the following rog 5 1 9 5 9 q and are defined as follows 0 0 6 X

The one to one functions g and h are defined as follows g 3 1 2 0 3 9 9 7 h x x 13 11 Find the following x 0 n 2 8 X

8 A fund manager wants to know if it is equally likely that the Dow Jones Industrial Average wi Il go up each day of the week For each day of the week the fund manager observes the followin g number of days when the Dow Jones Industrial Average goes up Day of the Week Observed Monday Tuesday Wednesday Thursday Friday 190 192 200 203 215 At the 10 significance level the critical value is and your test statistics is

The plot below shows the graph of g 1 JO 148 1 0 AA 6 Click on the plot above to open the image in another window G t has local maximum at t local minimum at t absolute maximum at t 11

Find all other zeros of P x x 10x 42x 72 given that 3 31 is a zero If there is more than one zero separate them with commas 0 i 0 0 Mp

Write a quadratic function h whose zeros are 6 and 5 h x

Consider the following power series x 1 n 1 n 8 Find the radius of convergence and the interval of convergence and identify if it is interval of absolute convergence or conditional convergence

x t 3e e 2t e e t and f t Compute a x t b x t f t c x t f t dt 9t e

This question 1 point s possible Find the standard form of the equation of the parabola satisfying the given conditions Vertex 6 1 Focus 6 2 The standard form of the equation is Type an equation Simplify your answer

2 cos 2 OA 2 cos 5x 8 Write the following expression as the sine cosine or tangent of a double angle Sele in the answer box to complete your choice OB 2 cos Simplify your answer Type an exact answer using as needed Use integers or fra expression OC 2 cos 1 2 5 8 2 5x 8 25 8 1 cos 1 sin 1 tan The exact value of the given expression is

Use an identity to solve the equation on the interval 0 2x 1 sin0 2 cos 20 What is the solution in the interval 0 2 Select the correct choice and fill in any a OA 9 Simplify your answer Type an exact answer using as needed Type your fractions for any numbers in the expression Use a comma to separate answ OB There is no solution

This question 1 point s possible The following equation involves a trigonometric equation in quadratic form Solve the equation on the interval 0 2x 2 cos2x 3 cos x 1 Select the correct choice below and if necessary fill in the answer box to complete your choice OA Submit test X Type an exact answer using as needed Use a comma to separate answers as needed Use integers or fractions for any numbers in the expression OB There is no solution