Calculus question and answers for January 02, 2024
- Q A 5 5 foot tall woman walks at 5 ft s toward a street light that is 16 5 ft above the ground What is the rate of change of...
- Q Find the derivative of the function by using the definition y 6x 7x 11
- Q 7 Write the equation of the following function 10 tay x 1
- Q Use the definition to find an expression for the instantaneous velocity of an object moving with rectilinear motion according to the given function relating s in ft and t in...
- Q Find the average rate of change of y with respect to x from P to Q Then compare this with the instantaneous rate of change of y with respect to...
- Q Find the derivative dy dx 9 5 y 10x 0 5x
- Q 7 Find g t for the function g t
- Q Differentiate dy dx 3 y 4x 16x 16x 64x 7
- Q A 11 2 resistor and a variable resistor of resistance R are placed in parallel The expression for the resulting resistance RT is given by RT value of RT as...
- Q ind all solutions to the differential equation xy y x y 0 x 0
- Q Determine the values of x for which the function f x Where is the function continuous or not continuous 4 2 4X is continuous If the function is not continuous...
- Q ompute the following limits using I H opital s rule if appropriate Use INF to denote and MINF to denote x mx 0 X 3 512 2 3 dt
- Q 2 The area of a circle increases at a rate of 6 cm s a How fast is the radius changing when the radius is 4 cm b How fast...
- Q A piston is seated at the top of a cylindrical chamber with radius 3 cm when it starts moving into the chamber at a constant speed of 7 cm s...
- Q Find values of the trigonometric functions of the angle in standard position whose terminal side passes through the given point 4 3 sin 0 cos tan 0 cot 0 3...
- Q Find the general solution to the differential equation dy dx ex 2y
- Q B 140 D A ADI BC m ACB 80 m ABC 40 M BAD 8040
- Q Determine the value of the unknown 1 log 3 27 X
- Q The electric current i in mA in the circuit i 8 7 1 e 0 37t where t is the time in s Evaluate i for t 7 0 ms...
- Q A 13 foot ladder is leaning against a vertical wall see figure when Jack begins pulling the foot of the ladder away from the wall at a rate of 0...
- Q An angler hooks a trout and reels in his line at 3 in s Assume the tip of the fishing rod is 13 ft above the water and directly above...
- Q By means of the definition of a radian change the given angles in radians to an equal angle expressed in degrees 4 498 rad O 4 498 rad Round to...
- Q complete a Sketch at least 2 cycles of the graph showing the height of a rider above the ground as a function of time if the rider gets on at...
- Q A rocket burns up at the rate of 5 tons min after falling out of orbit into the atmosphere If the rocket weighed 5400 tons before reentry express its weight...
- Q A rectangle initially has dimensions 2 cm by 5 cm All sides begin increasing in length at a rate of 2 cm s At what rate is the area of...
- Q Evaluate the given function f x 3x 1 find f x 3 f x 3 f x 3 f x 3 Simplify your answer
- Q A rope passing through a capstan on a dock is attached to a boat offshore The rope is pulled in at a constant rate of 2 ft s and the...
- Q Once Kate s kite reaches a height of 57 ft above her hands it rises no higher but drifts due east in a wind blowing 6 ft s How fast...
- Q Find the y derivative of the function by using the definiti y 2x 5x
- Q The volume of a cube decreases at a rate of 0 2 ft min What is the rate of change of the side length when the side lengths are 7...
- Q An inverted conical water tank with a height of 16 ft and a radius of 8 ft is drained through a hole in the vertex at a rate of 5...
- Q The population of a colony of mosquitoes obeys the law of uninhibited growth Use this information to answer parts a through c a it iN is the population of the...
- Q A thermometer reading 10 C is brought into a room with a constant temperature of 32 C If the thermometer reads 17 C after 2 minutes what will it read...
- Q 1 Given f x 3x and g x x 4 determine the expression for f g x 3 marks
- Q 2 Solve each of the following a f x x 5x 2x 24 5 marks
- Q Determine the volume of the largest rectangular box in the first octant with three faces in the coordinate planes one vertex at the origin and its opposite vertex in the...
- Q 8 Solve 2 logw 7 logw log w 10 0 Hint simplify the question by replacing the variable
- Q 6 As a tornado moves its speed increases The function S d 93 log d 65 relates the speed of the wind S in miles per hour near the center...
- Q a log4 log 10 000 log 32 4 marks
- Q c 73x 1 560 4 marks decimal answer
- Q d Determine the remainder when f x x 3x x 5 is divided by x 2 3 marks
- Q Part 4 of 5 Similarly Part 5 of 5 1000 81 Since Irl We can now see that 9 10 10 9 100 9 10 9 Submit Skip you cannot...
- Q Determine whether the series is convergent or divergent 1 57 87 n 1 O convergent O divergent If it is convergent find its sum If the quantity diverges enter DIVERGES
- Q Part 3 of 5 In the series 9 10 100 9 Part 4 of 5 9 Similarly 1000 81 81 1000 81 the ratiO If this is to equal ar...
- Q n 1 n 1 2 4 3 4 5 6 7 8 9 10 6 4 2 Sn MIRAS 6 2500 Graph both the sequence of terms and the sequence...
- Q Let an 4n 2n 1 a Determine whether a is convergent O convergent O divergent b Determine whether an is convergent n 1 convergent CO O divergent
- Q In our series 9 10 100 9 1000 81 the ratio 1000 81 100 9 is r
- Q Part 1 of 5 9 10 To see 9 10 100 9 100 9 1000 81 1000 81 as a geometric series we must express it as 00 00 n...
- Q Find 10 partial sums of the series Round your answers to five decimal places n 1 n 25 4 1 2 3 4 5 6 7 7 Sn
- Q Therefore we have the following If an answer does not exist enter DNE 6n lim 24 1 2 60 II lim eln y n
- Q Cancelling T from the numerator and denominator gives us lim In y lim x 00 X 54
- Q If y 1 2 x then In y Part 2 of 5 We can re write 6x Part 3 of 5 6x In 1 Now lim In y lim X...
- Q Part 1 of 5 an 2 1 If y 1 2 A Part 2 of 5 r n 1 2 then In y In 1 We can re write 6x...
- Q Tutorial Exercise Determine whether the sequence converges or diverges If it converges find the limit 6n Part 1 of 5 an If y 1 2 916x X then In y...
- Q 8 points Transform the differential equation 3 2r 5r 3r etsint into an equivalent system of first order differential equations and write the obtained system a matrix vector form
- Q An isotope of strontium Sr has a half life of 25 years Find the mass of Sr that remains from a sample of 30 mg after years Om 30e t...
- Q population is 5000 Find an expression for the number of bacteria after t hours OP 100 25t OP 100e OP 100e In 25 t OP 5000et Question 8 In 50...
- Q A bacteria culture starts with 100 bacteria and the growth rate is proportional to the number of bacteria After 2 hours the population is 5000 Find an expression for the...
- Q Solve the differential equation dy y 6z y Please show your work to receive full credit
- Q Given that all members of the family y Ce are solutions of the differential equation y 3x y find a solution that satisfies the initial condition y 0 15 O...
- Q All members of the family y Ce are solutions of the differential equation y 2xy True False
- Q Question 1 The function y x sin x is a solution of the differential equation y y 2 cos x True 2x sin x
- Q Find t t and B t vectors of the following vector functions a F t sint 2 cost sint b r t e sint e cost e at t 0...
- Q 110 101 101 101 Find and parameterize the set of all least squares solutions to this system 6 5 points Consider the inconsistent system A16 where A and b 3...
- Q 1 point Let y be the solution of the initial value problem The maximum value of y is y y sin 2x y 0 0 y 0 0
- Q Consider the scalarfield z f x y 0 5x y xy xy defined on the triangle with the corners A 2 2 B 4 1 and C 2 1 Determine...
- Q 1 point Consider the initial value problem my cy ky F t y 0 0 y 0 0 modeling the motion of a spring mass dashpot system initially at rest...
- Q a Find a particular solution to the nonhomogeneous differential equation y 6y 16y ex b Find the most general solution to the associated homogeneous differential equation Use c and c...
- Q 1 point A 10 kilogram object suspended from the end of a vertically hanging spring stretches the spring 9 8 centimeters At time t 0 the resulting mass spring system...
- Q 6z 6z 140 z 5 3z 5 Determine the correct partial fraction decomposition for the expression above Provide your answer below
- Q a r t b r t and c r t r t 19 r t t i 3 Answer a 3t i tj b 6ti j c 18t t
- Q entiation of Vector Valued Functions In Exercises 3 4 5 6 7 8 9 and 10 find r t r to and r to for the given value of to...
- Q For the following right triangle find the side length x 12 X 35 0
- Q Find the centroid of the region bounded by the xy plane the cylinder x y 2401 and the 1 Assume the density of 8 x y z 1 Use symbolic...
- Q 9 r t F t X G t where nswer 0 F t sin ti cos tj G t sin tj cos tk
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