Calculus question and answers for January 24, 2024
- Q Consider the functions A y x B y x n C y x n where n is an integer greater than 1 n 2 3 4 Which of these functions...
- Q 440 MATHEMATICS 8 12 17 20 24 29 1 2 C 9 x x 1 C x 4 x 8 C 32 log x 1 m log e e C...
- Q the Derivation of cartesian form from vector form Let the coordinates of the given point A be x y z and the direction ratios of the line be a b...
- Q To say that where A is and B is 5 5 2 is the same as saying is in the closed interval A B
- Q Consider the four functions graphed in the figure below and assume the equations for A B C and D can all be written in the form y abt Which two...
- Q A particle is moving along the curve y 3 4x 1 As the particle passes through the point 2 9 its z coordinate increases at a rate of 3 units...
- Q Let f x 2x cos 2x f z 4x cos 2x 4x sin 2x f 5 20 cos 10 100 sin 10 2 4 cos 2 16 sin 2x 18x...
- Q Let y tan 2x 5 Find the differential dy when z 5 and dz 0 4 0 8574 Find the differential dy when z 5 and da 0 8 1...
- Q Given the piecewise function defined by 3 x if x 1 H x x 1 if 1 x 3 x 3 if x 3 What is the value of H...
- Q hatch the functions with their graphs Enter the letter of the graph below which corresponds to the function Click on image for a larger view OD A OD 1 y...
- Q Let r x tan x Which of the following best describes its fundamental algebraic structure A A composition f g x of basic functions B A sum f x g...
- Q Three are functions one is not Identify the graph that is not a function OB OA OC 654 3 di N 3 2 2 OD N O
- Q Find the first derivative of 2x 1 4x In 2 f x tan
- Q If f x 4 tan 6 sin 4x find f x 96 cos 4x 1 36 sin 4x
- Q If f x 2 arctan 4x find z 8 1 16x Find f 4
- Q omework A cave with beautiful prehistoric wall paintings was discovered Some charcoal found in the cave contained 15 of the constant for 14C is 00012 The cave paintings are years...
- Q K After t hours there are P t cells present in a culture where P t 5000e0 2t a How many cells were present initially Give a differential equation satisfied...
- Q Which of the following functions are one to one Explain how you know a The function h graphed below b The function p graphed below
- Q a Find the formula for P t P t 12e 0 027t Type an expression using t as the variable b What is P 0 P 0 12 c What...
- Q A sample of radioactive material decays over time measured in hours with decay constant 2 The graph of the exponential function y P t shown on the right 5 gives...
- Q Part 1 of 9 a Find the formula for P t P t Type an expression using t as the variable Points 0 of 1 A sample of 12 grams...
- Q mework c How fast was the sample decaying after 6 hours d When was the sample decaying at the rate of 2 grams per hour a After 1 hour there...
- Q omework Part 3 of 3 a Find the formula for P t P t 4e0 04t Type an expression using t as the variable b What was the initial population...
- Q After t hours there are P t cells present in a culture where P t 5000e0 2t How many cells were present initially Give a differential equation satisfied by P...
- Q Points 0 of 1 At the beginning of 1990 22 3 million people lived in the metropolitan area of a particular city and the population was growing exponentially The 1994...
- Q Part 2 of 3 a Find the formula for P t P t 4e0 04t Type an expression using t as the variable b What was the initial population that...
- Q Points A company invests 20 000 in a CD that earns 9 compounded continuously How long will it take for the account to be worth 30 000 The account will...
- Q Homework A sample of radioactive material disintegrates from 4 to 3 grams in 50 days After how many days will just 2 grams remain days 2 grams will remain after...
- Q Five thousand dollars is deposited into a savings account at 7 5 interest compounded continuously a What is the formula for A t the balance after t years b What...
- Q When time is measured in days the decay constant for a particular radioactive isotope is 0 14 Determine the time required for a confined sample of the isotope to fall...
- Q A surveyor wants to know the length of a tunnel built through a mountain According to her equipment she is located 325 meters from one entrance of the tunnel at...
- Q A lighthouse sits at the edge of a cliff as shown A ship at sea level is 550 meters from the base of the cliff The angle of elevation from...
- Q Homework Part 1 of 3 a Find the formula for P t P t Type an expression using t as the variable Points 0 of 1 Let P t be...
- Q Looking up Boris sees two hot air balloons in the sky as shown He determines that the lower hot air balloon is 515 meters away at an angle of 15...
- Q Find x the angle of depression from the top of a lighthouse that is 165 ft above water level to the waterline of a ship 1143 ft off shore Round...
- Q A ramp 22 ft long rises to a platform The bottom of the platform is 13 ft from the foot of the ramp Find x the angle of elevation of...
- Q Rewrite the following expression in terms of exponentials and simplify the result as much as you can 5 sinh 5 In x 5 sinh 5 Inx Simplify your answer Use...
- Q A 12 ft ladder leans against the side of a house The top of the ladder is 10 ft off the ground Find x the angle of elevation of the...
- Q plane is 120 mi north and 194 mi east of an airport Find x the angle the pilot should turn in order to fly directly to the airport Round your...
- Q Evaluate csch 10x 4 esch 10x 1 dx 9 9 dx
- Q 3 sinh 2 In x Simplify your answer Use integers or fractions for any numbers in the expression D
- Q Find the derivative of y with respect to x F 5 y 3 sinh The derivative of y with respect to x is
- Q Evaluate S sinh 10x dx sinh 10x dx
- Q Solve the differential equation dy dx 11 1 2 y cos y
- Q Find the equation for a the tangent plane and b the normal line at the point Po 1 1 e on the surface 2x ln y y ln z X...
- Q dL The intensity L x of light x feet beneath the surface of the ocean satisfies the differential equation dx From experience a diver knows that diving to 19 ft...
- Q 3y 7y 4e X Is the function y e Yes No 7 3 x a solution of 3y 7y 4e Choose the correct answer below 4 c Find 3y 7y...
- Q A kite is flying 83 ft off the ground and its string is pulled taut The angle of elevation of the kite is 56 Find the length of the string...
- Q The length of a shadow of a building is 56 ft when the sun is 64 above the horizon Find the height of the building Round your answer to the...
- Q Is the function y ex a solution of 3y 7y 4e X Choose the correct answer below Yes No Batt b Find 3y 7y and 3y 7y for y e...
- Q Suppose that the bacteria in a colony grow unchecked according to the Law of Exponential Change The colony starts with 1 bacterium and triples in number every 30 minutes How...
- Q Find x Round your answer to the nearest tenth of a degree 15 A X
- Q Solve the differential equation dy dx 11 1 2 y cos y COS The solution is
- Q Find x Round your answer to the nearest tenth of a degree X 12 x
- Q Solve the differential equation dy 8x 4 y 2 y 2 dx The solution is
- Q Find x Round your answer to the nearest tenth of a degree 11 15 X x
- Q Check whether each of the following functions is a solution of the differential equation 3y 7y 4e x X b y e e 7 3 x a y ex c...
- Q Find dy dt y cos nt 13
- Q Find x Round your answer to the nearest tenth of a degree 10 14 x x
- Q 0 13 Points DETAILS A graphing calculator is recommended a How is the number e defined SCALCET9 Oe is the number such that lim h 0 Oe is the number...
- Q 63 78 Find the derivative of the function Simplify where possible 63 f x sin 5x 65 y tan x 1 64 g x sec e 66 y tan x
- Q larger x value 13 0 13 Points Draw a diagram to show that there are two tangent lines to the parabola of y x that pass through the point 0...
- Q Find an equation for the plane that is tangent to the surface z In x y at the point P 0 1 0 Using a coefficient of 1 for z...
- Q 4 Suppose that f 4 2 g 4 5 f 4 6 and g 4 3 Find derivative h 4 in a d a h x 3f x 8g x...
- Q a Find the velocity and acceleration as v t a t b Find the acceleration in m s2 after 9 seconds m s c Find the acceleration in m s2...
- Q 1 Evaluate the limit if it exists otherwise give the reason why the limit does not exist a lim cos 2 N 1 b lim 4x x 2x
- Q 12 0 13 Points DETAILS SCALCET9 3 1 064 O At what exact point on the curve y 7 2e 5x is the tangent line parallel to the line 5x...
- Q 1 log 1 x C 4 cos cos x C 440 8 12 11 x 4 x 8 C 3 14 17 2 6 ax b C 7 x 2...
- Q 1 4 7 10 12 14 6 440 cos2x 8 1 ax b 3a 1 3 3 16 x 3sinx e C 18 tan x sec x C 12 2...
- Q 29 32 Find y and y 29 y x ln x 31 y In sec x In x 1 ln x 32 y In 1 ln x 30 y
- Q 2 26 Differentiate the function 2 g t In 3 1 3 f x ln x 3x 5 5 f x sin In x 7 f x In x 9...
- Q 3 5 11 log 15 3 2 2 tan 2x C 2 x x 4x 5 6 7 x 1 log x x 1 C 8 log x x a...
- Q 10 g t 1 In t
- Q Evaluate the limit using L Hopital s rule lim 3 cos 52 sec 7x
- Q a If the symbol x denotes the greates integer function defined in this example evaluate the following If an answer does not exist enter DNE i lim 12 ii lim...
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