Calculus Questions

Does the sequence a converge or diverge Find the limit if the sequence is convergent a 2 1 Select the correct choice below and fill in any answer boxes within your choice OA The sequence converges to lim n c Simplify your answer OB The sequence diverges an 0 of 12

Suppose that Find f x and then evaluate f at x 1 0 f 1 3x 1 f x 2x 1

This problem tests calculating new functions from old ones From the table below calculate the quantities asked for 64 3 0 2 1 62 528385 64 1 21 4 480501 f x g x 524418 62 2 22 6 476782 f x 24704 60 0 28 8 23188 g x 24578 56 2 26 8 23066 f 0 g 0 5 If h x f g x calculate h 3 f g 0 f f 3 f g 0

Let F x f f x and G x F x You also know that f 6 8 f 8 2 f 8 14 and f 6 14 Find F 6 and G 6

2 If f x x 1 and g x 3 4x then gof 1

4 21584936490539 The answer above is NOT correct Find the area inside one leaf of the rose 1015 T 1 sin 50 240

Which of the following can be converted to the form a b I c COS X 2 sinx 1 d 2x 1 x2 x 1 x 1 1 e ex ex 2 dx dx dx dx n 1 1 19 W dx dw using a substitution

Find the area inside one leaf of the rose The area is leulator Turn in a sketch of the curve r 1 sin 50

Find the area inside one leaf of the rose The area is Turn in a sketch of the curve r 1 sin 50

Find the length of the polar curve given by r 7e0 40 on the interval 0 0 Answer Graph the curve on a calculator Turn in a sketch of the curve

The domain of f is 0 00 Type your answer in interval notation b Choose the correct graph of f Ay A The horizontal asymptote of f is y 5 Simplify your answer OB There is no horizontal asymptote the inverse of f Ay d Find f f x Simplify your answer G C c From the graph determine the range and any asymptotes of f The range of f is 5 00 Type your answer in interval notation Determine the horizontal asymptote of f if it exists Select the correct choice and if necessary fill in the answer box to complete your choice C Q OD Clear all

implify 2x 3x 5

2 Three step Adams Bashforth method Consider the interpolation nodes t 2 1 t where t t j jh a Write down the Lagrange interpolation polynomial P t for the function f t y t at the nodes above b Consider the IVP y t f t y t integrate the Lagrange polynomial P t from a exactly to determine bi b and b3 such that Yi 1 yih b f ti Yi b f ti 1 Yi 1 b3f t 2 2 As usual y denotes the value of y t at t tk Your answers b should be given as fractions Hint you may note for b we have f L t dt 2h evaluate the integral and do the same for b2 b hb pti 1 S t ti 1 t t 2 dt

Find the exact average value of f x x 4 NOTE Give an exact answer 1 x 1 The average value of f x on 0 x 4 is on the interval x 0 to

Indicate whether substitution is appropriate for each of these integrals If so evaluate the integral and enter the answer in the box that appears a fasina sin dx Choose one b fa sin sina da Choose one

Find the integral given below Check your answer by differentiation e 14e 148 e e 148 da C

eve gral given below Check your answer your answer by differentiation C

Use integration by substitution and the Fundamental Theorem to calculate the definite integral NOTE Enter the exact answer S X o 1 x 2 dx 4 5

Use the Fundamental Theorem to calculate the definite integral below NOTE Give an exact answer So 2x x 1 dx

Current Attempt in Progress Use integration by substitution and the Fundamental Theorem to evaluate the definite integral 13x x 1 dx Enter the exact answer 13x x 13x x 1 dx

Find all values of x satisfying the following conditions x 5 x 9 2 Y23 and y y 1 3 Select the correct choice below and if necessary fill in the answer box to complete your choice A The value s of x for which y y 1 is are Type an integer or a simplified fraction Use a comma to separate answers as needed OB Y y 1 for all values of x There are no values of x for which y y 1

Consider the function f x x 6x on the closed interval 1 3 Find the exact value of the slope of the secant line over the interval m By the Mean Value Theorem there exists c in 1 3 so that m f c Find all values of such c in 1 3 Enter exact values If there is more than one solution separate them by a comma C

Consider the function f x over the interval 2 2 e4x Does the extreme value theorem guarantee the existence of an absolute maximum and minimum for f on this interval Select the correct answer below Yes No

1a A snowball melts so that its surface area decreases at a rate of 0 5 cm min Find the rate at which the radius decreases when the radius is 4 cm SA 4nr 1b A water tank filtration plant is built in the shape of an inverted cone with height 5 2 m and diameter 5 m at the top Water is being pumped into the tank at a rate of 3 3 1 2 m min find the rate at which the water level is rising when there is 8 m of water V h Find the equations of the tangent lines to the curve y x x 2 that pass through 1c the point 3 2 Include a sketch to illustrate your solution

2 Find the equations of the tangent lines to the curve y x x 2 that pass through he point 3 2 Include a sketch to illustrate your solution 7 marks

A water tank filtration plant is built in the shape of an inverted cone with height 5 2 m and diameter 5 m at the top Water is being pumped into the tank at a rate of 3 1 2 m min find the rate at which the water level is rising when there is 8 m of water V h 7 marks 3

Find the derivative of the function g x jaomani g x ex x 4 smal questi Add Work I et 3 4x You can retry this q

C x 120 6x find the marginal average cost when 10 units are proc

B Find the range of a values for which the profit is positive Find the percentage rate of change of f x 102 28x at x 5 rounded to the nearest

Find the area of the region inside r 10 sin 0 but outside r 2 Graph the curves on a calculator Turn in a sketch of the curve

Find the area of the region bounded by the polar curve r 6e on the interval T 0 2

Find the area inside one leaf of the rose r 1 sin 5

Solve the system with the addition method 7x 5y 10x 9y Answer x y 33 49 Enter your answers as integers or as reduced fraction s

d The negative angle closest to zero that satisfies cos 0 3 7 is

V Find the sum of the x and y intercepts of any tangent line to the curve x y 10

Find the sum of the and y intercepts of any tangent line to the curve x y 10

If log x 15y x y 3 and y 4 1 find y 4 by implicit differentiation 4 1 An equation of the tangent line to the curve at the point 4 1 is

Find the sum of the x and y intercepts of any tangent line to the curve x y 10 FEB

Find y x y dy da dax by implicit differentiation Note unfortunately WeBWork isn t quite smart enough to understand that x y for this problem is the same as ex y After differentiating d simplify beyond solving for dy

dr Let A be the area of a circle with radius r If dt dA dt 2 find when r 2

Find by implicit differentiation dy 1 dx tan x y Y 1 x dy da Remark once again WeBWork isn t quite smart enough to understand all correct answers Carry through the differentiation and solve for in the simplest way possible

Compute the following derivative d dx cot cot

A thermometer reading 12 C is brought into a room with a constant temperature of 25 C If the thermometer reads 17 C after 4 minutes what will it read after being in the room for 7 minutes Assume the cooling follows Newton s Law of Cooling U T Uo T ekt Round your answer to two decimal places 24 57 C 8 77 C 30 56 C 19 44 C QUESTION 20 rabbit

is a radioactive material that decays according to the function A t Age scientist has a sample of 800 grams of strontium 90 a What is the decay rate of strontium 90 b How much strontium 90 is left after 20 years c When will only 200 grams of strontium 90 be left d What is the half life of strontium 90 a The decay rate of strontium 90 is 2 44 Type an integer or a decimal Include the negative sign for the decay rate b Approximately 491 grams of strontium 90 is left after 20 years Do not round until the final answer Then round to the nearest whole number as needed c Only 200 grams of strontium 90 will be left in about 56 8 years Do not round until the final answer Then round to the nearest tenth as needed 0 0244t d The half life of strontium 90 is approximately years Do not round until the final answer Then round to the nearest tenth as needed 1 Points 0 5 of 1 15 points where Ao is the initial amount present and A is the amount present at time t in years Assum

x 2 1 000 3 or 2 3 3 00 3 2 QUESTION 18 Solve the problem A fossilized leaf contains 35 of its normal amount of carbon 14 How old is the fossil to the nearest year Use 5600 years as the half life of 28 672 3474 8466 33 664

Find the following derivatives a dx arcsin x b arctan e dx Use inverse trigonometric functions to solve the following trigonometric equations c If the angle is known to be in the interval and 3 sin 2x 2 then x d The negative angle closest to zero that satisfies cos 0 3 7 is

Compute the following derivative d cos EEE

If z x y with x 0 d 2 and d 5 find when x dt 8 and y 15 Answer dz dt

Find the derivative of the function It may be to your advantage to simplify before differentiating f x cos arcsin 52 SE3

QUESTION 19 Solve the problem A thermometer reading 12 C is brought into a room with a constant temperature of 25 C If the thermometer reads 17 C after 4 minutes what will it read after being in the room for 7 minutes Assume the cooling follows Newton s Law of Cooling U T Uo T ekt Round your answer to two decimal places 24 57 C 8 77 C 30 56 C 19 44 C QUESTION 20