Vector Calculus Questions and Answers

tree diagram to find the number of ways 3 letters can be chosen from the set P Q R if order is repetition is allowed no repeats are allowed ind the number of combinations of 3 elements taken 3 at a time Does this answer differ from the 5 repetition is allowed how many ways can 3 letters be chosen from the set P Q R if order is imp orrect formula below and if necessary fill in the answer boxes to complete your choice the terms of your expression in the same order as they appear in the original expression 3C3 M 3P

Please indicate whether this proportion is true or false 12 144 8 96 The proportion is True False

Write the given ratio in the following word statement Please include the units Howard walks 5 km every 2 days km days

Siven the graphs of f x and g x below find the composition of functions f g 0 Do not type f g 0 in your answer Provide your answer below 4 2 1 4 3 0 1 f x 01 g x

mutations to solve udent activity club at the college has 22 members In how many different ways can the president a treasurer and a secretary ute values into the formula for Pr

e multiplication principle to solve o manufacturer produces 8 models each available ferent colors with 4 different upholstery fabrics nterior colors How many varieties of car are le O Points 0 of The manufact varieties of car

ind the expected value for the random variable whose robability function graph is displayed here What is the expected value of the random variable 3 Type an integer or a decimal

Points 0 of vo fair dice are rolled find the probability that the sum of the dice is 6 given th probability is nplify your answer Type an integer or a simplified fraction

Find a sequence of elementary matrices that can be used to write the matrix in row echelon form 1 2 1 0 036 3 5 10 7 0 1 H 1 0 O 0 1 0 0 1 2 0 100 0 1 0 5 0 1 O 01 30 0 1 0 0 i 0 0 1 50 1 0 1 00 1 0 0 1 0 0 0 1 0 50 1 illa 11 1 0 0 1 0 0 0 1 0 0 0 1 2 0 1 0 0 1 0 0 1 3 0 0 1 0 i 501 0 1 3 0 1 0 0 1 0 0 0 1 0 0 ell 1 3 0 0 1 0 0 1 2 100 010 0 1 3 0 0 1 0 1 0 0 0 1 0 0 0 1 2 I 100 0 1 0 5 0 1 1 0 0 0 1 0 0 0 1 2

Find the bearing from O to A N W O 700 E The bearin

domain 4 4 that satisfies the hypotheses of the Mean Value Theorem and the conclusion of the Mean Value Theorem at and x 2 graph x 3 M5b Sketch the graph of a function on domain 4 4 that fails at least one of the hypotheses of the Mean Value Theorem resulting in a graph that does not satisfy the conclusion of the Mean Value Theorem

Susan s dog Lilly weighs 3 8 pounds Round this number to the nearest whole number ones place Lilly weighs about pounds A 2 B 4 C 3 D 38

Function Yes or no Why If yes find the Domain and Range A 1 2 2 7 5 7 B 1 2 3 5 3 8 C x y 16 r

Find the equation of the tangent line to the graph of f x 3 x at x 49 Express numbers in exact form Use symbolic notation and fractions where needed Let y f x and give the equation in terms of y and x equation

Classify each function as a constant function a power function a sum of functions or a difference of functions Constant function f x x 2 f x 9 Power function f x x 2 Answer Bank Sum of functions f x x x f x x x Difference of functions f x x f x x

Convert the angle to a decimal in degrees 8 8 8 8 8 8 Do not round until the final answer Then round to two decimal places as neede

GI Given Tunction of two variabi a y x 2 y 2 e left x 2 y 2 right text a Sketch the graph of the function f b Find a tangent plane to the graph of the function f les T X at all points x y f x y c At what points is the tangent plane parallel to the xy plane How does the function behave near the points 0 0

Use a change of variables to evaluate the following definite integral H 3 H 4 sin x 2 COS X u cos x What is the best choice of u for the change of variables Find du du T 3 S T sin x dx Rewrite the given integral using this change of variables dx sin x cOS X dx JO Type exact answers du

In the following figure estimate the slopes of all line segments If an answer is undefined enter UNDEFINED a m b m c m d m e m f m 9 m h m i m a b g c h d 0

Find the equation of the given linear function f x X 5 0 5 25 f x 4 5 6 10

Given the following graph identify the key features Y intercept 3 X intercept Domain Range Max Min F End Behavior Increasing Decreasing Positive Negative I

A point on a line and its slope are given Find the point slope form of the equation of the line P 4 1 m 0 The point slope form of the equation of the line is Do not simplify Use integers or fractions for any numbers in the equation

f x sin x a Sketch a clearly labeled graph of f x using a 1 1 scale b Explain why the slope of the tangent line to the graph of f at the origin x 0 is given by the limit lim x rightarrow 0 frac sin x x c Approximate the limit using a table of values d Use your result in c to find an equation for the tangent line to f at the origin and add a graph of it to

24 Harvesting fish A fish farmer has 5000 catfish in his pond The number of catfish increases by 8 per month and the farmer harvests 300 catfish per month a Show that the catfish population P after n months is given recursively by P 1 08P1 300 Po 5000 b How many catfish are in the pond after six months

The population of a suburb of New York City has shown a linear growth in the years 1990 2003 The population in 1990 was 36480 people and it has been growing at a rate of 245 people per year

Find the one sided limits whether lim 2 f x exists O 2 2 does not exist 2 2 exists and equals 2 O 3 3 exists and equals 3 3 3 does not exist lim x 2 f x and lim 2 f x from the given graph of fand determine

Find lim xaf x if it exists lim x a lim x a lim f x b f x a f x c The limit fails to exist

Graph the function and the indicated tangent line Graph f x 4x and the tangent line to the graph at the point whose x coordinate is 2

2x Given g x f cos t dt find g x O None of the above O 2sin x O cos 2x O2cos 2x

Write 94 as a traditional Chinese numeral Click here to view the Chinese numerals table Choose the correct traditional Chinese numeral below OA tu 8 OB 8 8 ti D 8

Write the Chinese numeral to the right as a Hindu Arabic numeral t t 5 8 9 10 100 1000 0 1 2 3 4 5 6 7

cot sin 6 COS seccot sin 1 sec81 sec 0 1 tan 0 1 cos 0 1 sec sec 0 cos 0

A population of cattle is increasing at a rate of 700 30 t per year where t is measured in years By how much does the population increase between the 12 th and the 18 th years

2 f x x 25 g x 2x Find the following f 5

6 If g x 9x 2 x 8 find the range of g x

Temperature Suppose there is a 1 1 F drop in temperature for every thousand fee that an airplane climbs into the sky If the temperature on the ground is 45 8 F wha will be the temperature when the plane reaches an altitude of 8 000 ft The temperature will be F Type an integer or a decimal

Convert to a decimal Round to 3 decimal places if necessary 75 4 12

Round to the nearest thousandth 2 1175

Please write as a decimal 84 100

Which function has the same range as f x 2 x 3 8 Og x x 3 8 g x x 3 8 O g x x 3 8 Og x x 3 8

What is the domain of the function y 3 x 1 0 X 0 0 1 x

Differentiate the function h x h x n x x 2

Define the points Q 5 3 and R 3 9 Carry out the following calculation Find the unit vector with the same direction as QR

Find the following vector The vector in the direction of 8 6 with length 4 The vector in the direction of 8 6 with length 4 is Simplify your answers

Sketch PT in blue and its corresponding position vector in red Choose the correct graph below OA x Q G OB P Ay 10 10 Q SOC X Q O D

Define the points P 5 1 Q 22 R 2 2 S 5 4 T 4 3 and U 5 4 Sketch QU PT and RS and the corresponding position vectors Sketch QU in blue and its corresponding position vector in red Choose the correct graph below O D OA Q OB Q Q Q 2 OC Q Q Q

A B C 220 Year 220 220 K gle 220 in standard position

26 Which of the following shows the angle 108 in standard position A OB O C D 55 3n

Determine whether the given function is linear If the function is linear express the function in the form f x ax the function is not linear enter NOT LINEAR f x 3x 5 NOT LINEAR f x

Find all real solutions of the equation Enter your answers as a comma separated list 8 7x 6 X