Calculus question and answers for February 28, 2024
- Q Consider the differential equation B y 1 Be sure not to round your calculations at each step Now use four steps with initial condition y 0 2 A Use linear...
- Q Suppose you have just poured a cup of freshly brewed coffee with temperature 90 C in a room where the temperature is 25 C Newton s Law of Cooling states...
- Q Numerically approximate the solution to the differential equation dB dt with initial value B 900 when t 0 Compute each value using linear approximation this method is also called Euler...
- Q Two lakes have populations of fish but the conditions are quite different in these lakes In the first lake the fish population is growing and satisfies the differential equation dy...
- Q Use Euler s method with step size 0 2 to estimate y 1 where y x is the solution of the initial value problem y 5x y y 0 1
- Q The radioactive isotope carbon 14 is present in small quantities in all life forms and it is constantly replenished until the organism dies after which it decays to stable carbon...
- Q Use Euler s method with the given step size to estimate y 1 4 where y x is the solution of the initial value problem y x xy y 1...
- Q Use the symbols provided below to fill in the phase line for the differential equation x x 3 x 1 To place a symbol on the line Click a symbol...
- Q For each of the following differential equations determine if the proposed function is a solution a Let C and k be constants Given the differential equation f t kf t...
- Q Is each of the following functions a solution to the differential equation y 11y 30y 0 Yes Ma 1 y 3ebm 2 y 6e 5w 3 y There are only...
- Q For what positive value of k does the function y sin kt satisfy the differential equation y 169y 0 For what negative value of k does the function y cos...
- Q Find all values of r so that the function y x solves the differential equation x y 6xy 14y 0 into the equation and find values of r that satisfy...
- Q Consider the slope field shown a For the solution that satisfies y 0 0 sketch the solution curve and estimate the following and v 1 y 1 b For the...
- Q The functions are all solutions of equation y x xy 2y 4x x 0 Find the constant c which produces a solution which also satisfies the initial condition y 5...
- Q In the spreadsheet pictured an arrow indicates the contents of a cell are copied down its column n the spreadsheet below column A holds different values of h and column...
- Q Match each differential equation to a function which is a solution FUNCTIONS A y 3x m B y e C y sin x D y t E y 7 exp...
- Q Each row of the spreadsheet below contains the position of a particle at a given time The times are stored in column B and the corresponding positions in column A...
- Q Consider the slope field shown a For the solution that satisfies y 0 0 sketch the solution curve and estimate the following and y 1 y 1 b For the...
- Q In the figure below which of the following is a solution to the differential equation dy dt with initial value y 0 3 4 Note pay attention to axis labels...
- Q Check by differentiation that y 5 cos 2t 5 sin 2t is a solution to y 4y 0 by finding the terms in the sum So 1 411
- Q Verify that every member of the family of functions y following questions Answer y log x C X 1 Find a solution of the differential equation that satisfies the initial...
- Q Which of the following functions are solutions of the differential equation y 3y 18y 0 Select all that apply 3x A y x B y x e C y x...
- Q Let y 16y 0 Find all values of r such that y separated list ker satisfies the differential equation If there is more than one correct answer enter your answers...
- Q This problem is an example of a differential equation an equation that relates a function to one or more of its derivatives You can solve this problem by doing some...
- Q Use the given graph of y f x to find the intervals on which f x 0 the intervals on which f x 0 and the values of x for...
- Q 8 Using the second derivative test find the maximum and minimum points for the function f x x 8x 5 What conclusion can be made if a A function changes...
- Q Helium is pumped into a spherical balloon at a constant rate of 3 cubic feet per second How fast is the radius increasing after 2 minutes At what time if...
- Q Find an equation for the parabola that has its vertex at the origin and has its focus at the point 8 75 0
- Q Use the curve sketching procedure to analyze the function a y x x 20x 1 x 1 x Determine the horizontal asymptote x 2x 6 2 x b y a...
- Q Find the vertex focus and directrix for the following parabolas x 2 8 y 2 Vertex Focus
- Q A drug that stimulates reproduction is introduced into a colony of bacteria After t minutes the number of bacteria is given approximately by the following equation Use the equation to...
- Q A T shirt manufacturer is planning to expand its workforce It estimates that the number of T shirts produced by new workers is given by T x 0 5x 18x...
- Q Find the intercepts of the function a f x x 2x 15 x 10 x 5 Determine if the function is even odd or neither b y a f x...
- Q The marketing research department of a computer company used a large city to test market the firm s new laptop The department found the relationship between price p dollars per...
- Q A drug that stimulates reproduction is introduced into a colony of bacteria After t minutes the number of bacteria is given approximately by the following equation Use the equation to...
- Q A drug that stimulates reproduction is introduced into a colony of bacteria After t minutes the number of bacteria is given approximately by the following equation Use the equation to...
- Q For each function determine i the critical values ii the intervals of increasing or decreasing iii the maximum and minimum points a f x 4x 12x 7 b f x...
- Q K Use the definition of the derivative to evaluate the limit 7 h 343 lim Im 1 0 7 h h Question 24 7 3 343
- Q Use both the washer method and the shell method to find the volume of the solid that is generated when the region in the first quadrant bounded by y x...
- Q Find the higher order derivative dx 6log x 4 6log x 4 Question 19
- Q OA If b 0 and b 1 then c If b 0 and b 1 then d X OB If b 0 and b 1 thenx logbx Inb OD If...
- Q K Evaluate the following integral dx x 11 x 0 dxa Question 21 7
- Q Find the higher order derivative 3x in 3x 3x in 3x 0 Question 20 7
- Q K Use the definition of the derivative to evaluate the limit lim Inx 6 x X 2 6 Type the exact value of the limit lim Inx 6 Question 23...
- Q K Evaluate the derivative of the following function H x 2x 5 H Question 16 7 3 61
- Q vative y sin 2x In sin 2x Y 0 Use parentheses to clearly denote the argument of each function www 17 7 3 65
- Q the following integral J5 1 5 1 Inxx dx fax 6 1 In xxx dx Type an exact answer in simplified form
- Q K Find the derivative of the following function yain x 8 dy dx Type an exact answer using it as needed Question 12 7
- Q of the function and evaluate the derivative at the given value of a f x sin x a Find the derivative of the function sin x x dx Use parentheses...
- Q Evaluate the derivative y 3x y Type an exact answer Question 15 7
- Q V Find the derivative of the following function y 22 sinx dx 22 s n x Question 5 7 3
- Q Evaluate the following integral 5 dx 4x 54 dx 4x 5 In 5
- Q y x 45 dy dx Type an exact answer using radicals as needed N
- Q WOWWW
- Q 11 214 the following integral 1Aa dp dp Type an exact answer 7 3
- Q K Solve the following equation Simplify your answer Use a comma to separate answers as needed
- Q X log 8 3 on for x Type an integer or a simplified fraction wwwwww
- Q shaped like a box is 60 m high with a face that is 70 m wide A strong wind blows directly at the face of the building exerting a pressure...
- Q section with a height of 7 m and horizontal sides of width m and 7 m Assume the length of the trough is 14 m See the figure to the...
- Q rentiation for the logarithmic function f x log x How does it differ from the derivative formula for Inx Which of the following is the rule of differentiation for the...
- Q e g The area between the curve y Part 5 of 7 Determine whether the following statements are true and give an explanation or counterexample Assume x 0 and 0...
- Q K Enhanced Homework a Find the critical points of f x 6x e b Use the First Derivative Test to locate the local maximum and minimum values c Determine the...
- Q a Find the inverse of the function below on the given interval and write it in the form y f x b Verify the relationships f f x x and...
- Q Part 1 of 5 JO 0 Type exact answers HW Score 48 8 11 71 of 24 points O Points 0 of 1 For large distances from the surface of...
- Q O Points 0 of 1 cross sections that taper linearly from a radius of 6 cm at the top of the glass to a radius of 5 cm at the...
- Q a Find the critical points of f x 6x e b Use the First Derivative Test to locate the local maximum and minimum values c Determine the intervals on which...
- Q O Points 0 of 1 Use the shell method to find the volume of the solid formed when a hole of radius 1 is drilled symmetrically along the axis of...
- Q are measured in meters Assume the water level is at the top of the dam termine the total force on the dam Lengths Oc w y 5 y OD w...
- Q The figure to the right shows the shape and dimension of a small dam Assuming the water level is at the top of the dam and that the shape of...
- Q Part 1 of 3 HW Score 48 8 11 71 of 24 points O Points 0 of 1 A diving pool that is 4 m deep and full of water...
- Q Part 1 of 3 Find the width function w y for each value of y on the face of the building w y Use integers or decimals for any numbers...
- Q Part 1 of 3 A glass has circular cross sections that taper linearly from a radius of 6 cm at the top of the glass to a radius of 5...
- Q K Use both the washer method and the shell method to find the volume of the solid that is generated when the region in the first quadrant bounded by y...
- Q Use a change of variables to evaluate the following definite integral 2 9 27v 9 9 0 27v 9 S dv dv Type an exact answer using radicals as needed
- Q 25 The lower edge of a dam is defined by the parabola y see figure Use a coordinate system with y 0 at the bottom of the dam to determine...
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