Calculus question and answers for January 10, 2024
- Q Find v t given the acceleration and initial condition v t Usage To enter a vector for example x y z type x y z a t 4i v 0...
- Q Find an equation of a plane containing the three points 5 3 2 3 6 3 3 7 1 in which the coefficient of a is 7 0
- Q Find the equation of the plane which passes through O and is parallel to 3y 2x z 6 y z 8 x
- Q Find an P 1 0 0 Q 0 3 4 R 0 2 3 equation of the plane through the three points given
- Q Find a vector n normal to the plane with the equation y 3x3z 4 n 3
- Q 52 Let f x x 1 if x 1 x 2 if x 1 a Find limx f x and limx f x b Does limx 1 f x exist...
- Q Find the area of the region bounded by the curves y x y 4 x y 2 and y 1 Hint You ll definitely have to sketch this one on...
- Q 11 34 Evaluate the limit if it exists 11 lim 3x 7 x 2 13 lim t 4 1 2t 8 t 4 15 lim x 2 17 lim x2...
- Q In Seattle on September 30 the temperature in F t hours after midnight was given by the function Temp t 60 12 sin t 11 What was the average temperature...
- Q Find the area of the region in quadrant I bounded by the curves y x 2 y x 2 y 1 and y 3 1 2 You get O A...
- Q Find the area between the curves y f x x 3x and y g x x 4x x on the interval 0 x 2 O A 200 OB B 83...
- Q Find the area of the region bounded by the curves 3 y sin x y csc x x 4 and x You get O A 2 2 OB 2 2...
- Q certain chemical involved in the reaction changes at a rate that s inversely proportional to the product of the mass of the chemical present in grams and the time elapsed...
- Q 5 Consider the differential equation y 1 x A Use the axes provided to sketch a slope field for the given differential equation at the eleven points indicated 2 points...
- Q 3 9 Evaluate the limit and justify each step by indicating the appropriate Limit Law s 3 lim 4x 5x x 5 5 lim v 2v 2v 5 v 2...
- Q 4 At high temperatures nitrogen dioxide NO2 decomposes into NO and O2 If y t is the concentration of NO2 in moles per liter then at 600 K y t...
- Q 1 The popu present population A Model the population P P 1 of the bacteria population with a differential equation B Solve the differential equation that models the population P...
- Q 3 The slope of a curve is equal to y divided by 4 more than x at any point x y on the curve A Find a differential equation describing...
- Q 1 Consider the curve y f x 2 1 A Find the exact area of the region in the first quadrant bounded by the curves y f x 2x and...
- Q How many definite integrals would be required to represent the area of the region enclosed by the curves y cos sin and y cos xsin 2 and y 0 03z...
- Q 3 A culture of bacteria is growing at a rate of 4e0 5 per hour within hours and 0 1 20 A How many new bacteria will be in the...
- Q Given that lim f x 4 x 2 find the limits that exist If the limit does not exist explain why a lim f x 5g x x 2 c...
- Q A Find the exact area of the region in the first quadrant bounded by the curves y f x 2x 1 and y x Exact area means no calculator numbers...
- Q Find a value of c 1 so that the average value of f x the interval 1 c is 0 9 A c 1 OB c 4 OC C 4...
- Q 4 Consider the functions f x x3 x4 1 and g x Let R denote the region in the first x 1 quadrant bounded by the curves y f x...
- Q 2 A particle moves on a coordinate line with an acceleration at time seconds of et 2 m sec2 At 1 0 the particle is at the origin and its...
- Q 1 Use the eigenvalue to find the general Method and eigen vector solution of the following finst onden system where x Ax Show all your work X 2X 5X2 X...
- Q 7 Solve the following initial value phroblem the Laplace Transform Alternate Use Show all work do not X x 12X 12x 0 10 Or methods
- Q lim lim x 2 3 lim In x 1 I 30 lim PEY F x 3 34 lim In sin x D limp
- Q 29 40 Determine the infinite limit 29 lim I 31 lim x 33 lim In x 1 33
- Q Powen to the following differential equation you do not senies to find the powen senies solution need to find the nadius do not need to find the familiare function You...
- Q hind the Invense function show Laplace Thansform as of Variable to fully simplity as all your work F s S 5 d 3 3 2s 2 16
- Q the given nonlinear system and associated critica Point find the Jacobian Matnix and use eigenvalues to classify the critical point in terms of type an Stability Then wonite out the...
- Q 19 22 Guess the value of the limit if it exists by evaluating the function at the given numbers correct to six decimal places x 3x x 3 x 9...
- Q 12 A race car is running practice laps in preparation for an upcoming race To judge how the car is performing the crew takes measurements of the car s speed...
- Q Below is a graph of two curves x y 3y the S shaped 5 in red Which definite integral should you use to compute the area enclosed by these two...
- Q 15 Water is draining from a small cylindrical tank into a larger one below it The small cylindrical tank has a radius of 4 feet and a height of 6...
- Q he formal integral Calculus definition Thans form to find the of the and Use of the Laplace Laplace Show all woonk FH eat Transform 1 following funct all propen nota
- Q You may use your calculator on the following three questions 11 Consider a curve given implicitly by the equation 1 x y xy 85 0 A Calculated at a general...
- Q 12200 4 Consider a lake of constant volume 12200 km3 which at time contains an amount y t tons of y 1 pollutant evenly distributed throughout the lake with a...
- Q signed area under the curve between 0 and x Note that on the left hand side of the the variable is x Ther on the right hand side is a...
- Q 13 14 Use the graph of the function f to state the value of eac limit if it exists If it does not exist explain why a lim f x...
- Q 17 Consider the differential equation given by A On the axes provided below sketch a slope field for the given differential equation at the nine points indicated B Let y...
- Q 16 Suppose that f has a continuous second derivative for all x and that f 0 1 f 0 2 and f 0 0 A Does f have an inflection...
- Q You may NOT use your calculator on the following three questions 14 S 4 3 2 H Let f x M 2 3 1 g x Let g be a...
- Q velocity by time it hits the ground By measuring the impact you determine that this terminal velocity is 49 m sec A Write the equation representing the velocity 1 of...
- Q 3 Biologists stocked a lake with 800 fish and estimated the carrying capacity of the lake to be 20000 In the first year the number of fish doubled Use a...
- Q Find an equation of the line below Slope is 3 3 6 on line What is an equation for a line that has a slope of 3 and passes through...
- Q K if f x 4 1 If f x compute f 2 and f 2 9 f 2 Simplify your answer 1 16 f 2 Simplify your answer
- Q 6 Find the slope of the tangent line to the curve y x 48 at x 7 Then write the equation of this tangent line 6 x 48 at x...
- Q something that is happening in the world over the last month I would like you to find something other than the fire in Maui Create a slides presentation Find 2...
- Q Consider the cost function C x 5x 14x 16 thousand dollars a What is the marginal cost at production level x 4 b Use the marginal cost at x 4...
- Q Compute the following 1 f 2 and f 2 when f t 2 t f 2 Type an integer or a simplified fraction
- Q Suppose the revenue from producing and selling x units of a product is given by R x 6x 02x dollars a Find the marginal revenue at a production level of...
- Q Find the first and second derivatives f P 7P 4 5 d dP f P 0
- Q Find the first and second derivatives y x 11 1 2 x 11 y y 0
- Q e 4 t cos 3 t 2 3 e 4 t sin 3 t e answer above is NOT correct 1 point Find the inverse Laplace transform f t F...
- Q 8 For the function A whose graph is shown state the following a lim A x b lim A x x x 3 c lim A x x 2 e...
- Q 7 For the function g whose graph is shown find a number a that satisfies the given description a lim g x does not exist but g a is defined...
- Q 3 Let F x 3r cos 1 2 dt A Using the First Fundamental Theorem of Calculus find F x Yes this is as easy as it seems B Starting...
- Q 4 Use the given graph of f to state the value of each quantity if it exists If it does not exist explain why a lim f x x 27...
- Q 4 The function has domain below IX B Find h y f 1 5x 2 which it is continuous A graph of y is given Define a new function h...
- Q beginning of a race Velocities of the two cars during the race are given in the tables below where velocities are in miles per hour and times are in seconds...
- Q 1 Explain in your own words what is meant by the equation lim f x 5 x 2 Is it possible for this statement to be true and yet f...
- Q If a rock is thrown upward on the planet Mars with a velocity of 10 m s its height in meters t seconds later is given by y 10t 1...
- Q Consider the piecewise defined function that is graphed above The point A 3 2 0 a Find the equation of the piecewise defined function graphed above You may assume that...
- Q 12 Let the function u t be defined by u t at b ct d with arbitrary real valued constant coefficients a b c d a Determine the domain for...
- Q 5 The deck of a bridge is suspended 275 feet above a river If a pebble falls off the side of the bridge the height in feet of the pebble...
- Q The point P 2 1 lies on the curve y 1 1 x a If Q is the point x 1 1 x find the slope of the secant line...
- Q A student bought a smartwatch that tracks the number of steps she walks throughout the day The table shows the num ber of steps recorded minutes after 3 00 PM...
- Q Write the slope intercept equation for the line having the given information 1 3 and 2 3 on the line What is the slope intercept equation of the line Use...
- Q 3 Use the power rule to find the derivative of f x x fi
- Q Estimate the price of one barrel of crude oil on January 25 2016 and the rate at which the price was rising on that day Your answer for the rate...
- Q pi 1 Find the derivative of f x 3 10 at x 3 10 Type an integer or a simplified fraction
- Q Find the slope of the graph of y f x at the designated point f x 2x 6x 2 3 2 The slope of the graph of y f x...
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