Calculus question and answers for October 11, 2023
- Q Draw six isoclines gradient curves for the differential equation x y and then make dy dx partial slope field by considering points on the isoclines
- Q 3 The plane passes through D 3 5 4 with normal 2 1 3 Determine the Scalar Form of the plane and the exact intercepts 5 marks
- Q x t sint cos 2t y t cost sin 2t Find x axis rotate
- Q 3 Consider the following models of harmonic motion Y 5 sin 2t 1 y2 5 sin 2t 3 Do both motions have the same frequency What is the phase for...
- Q One solution to an ordindary differential equation ODE is y 1 Which of the following direction fields could correspond to this ODE 2 12 X TI I 2VI Q Q...
- Q Consider the initial value problem u t u t u t 24 0 5 Although the differential equation associated with this problem is non linear the differential equation for y...
- Q Verify that for any value of c the function y ce 2 e is a solution to this ODE y 2y e then find the value of C for which...
- Q Consider this ordinary differential equation ODE dy dz At the point 1 0 5 the direction field for this ODE has a slope of YTA At the point 1 5...
- Q 11 2 1 dy dx dy dx 1 dy dx Which of the following equations would produce the direction field above dy dx x x y 1 x y x...
- Q If y x ek is a solution of this differential equation y 10y 24y 0 then the possible values of k are
- Q The solution to this initial value problem dy dx is u r 6x 5 y 2 5
- Q If r t k is a contant solution to this ordinary differential equation 8t dx dt then k 4x 4 0
- Q Problem 4 Find the radius of convergence of the following power series a b n 0 where d p n zn n 0 n in z n n p x...
- Q oof Use an algebraic degree measure The measure
- Q Use Laplace transform to solve the ODE f t f t u t 1 with initial condition f 0 1 where u t is the Heaviside ste function
- Q By directly applying the Cauchy Riemann equations show the following functions are analytic a f z z C 0 b f z ze c f z sin z
- Q 2 Let f x 3cosx 4sinx 5 TT a Determine the exact slope of f x at a 4 b Determine the tangent line approximation to y f x at...
- Q Find 1 10 if f x x x 8 10 Simplify your answer
- Q Find the power series solution for the differential equation y 3xy y 0 with the initial conditions y 0 2 a y 0 0 5 A y x 1 2...
- Q Set up but do not evaluate an integral for the volume of the solid obtained by rotating the region bounded by the given curves about the specified line begin array...
- Q Find the function y y x for x 0 which satisfies the separable differential equation dy 4 16x dx xy with the initial condition y 1 4 y x 0
- Q Consider the following 1 y a Find y by implicit differentiation y 6 X 7 b Solve the equation explicitly for y and differentiate to get y in terms of...
- Q dy Solve the separable differential equation 0 2y dx and find the particular solution satisfying the initial condition y 0 6 y x
- Q Find a function y x such that 3yy x and y 3 11 y HR
- Q 29 Suppose that y is a solution to the initial value problem y y2 1 e y and y 1 0 Show that 1 y t 1 for all t...
- Q Obtain the differential equations with the following General Solution Co2x
- Q 1 Classify each of the following equations as to order and degree a 3dy 4xy secx dx 0 b L d q dt R dq dt q C E t...
- Q If s1 2 and sn 1 p2 sn for n 1 2 3 prove that sn converges and that sn 2 for n 1 2 3
- Q 1 point Sometimes a change of variable can be used to convert a differential equation y y into a separable quation Une con technique is as follows 1 Consider a...
- Q Compare the graph of the function with the graph of f x arcsin x g x arcsin x 2 L 3 1 2 3 A 4 3 y I 2...
- Q Area of a quadrilateral Given a quadrilateral that has vertices x y x2 Y 2 X3 Y3 and x4 y4 given in a counter clockwise order the area enclosed by...
- Q ar Inequalities K The following graph shows the total wid in millions in the United States for the y idgets millions 10 8 6 United States Widget Production 11 4...
- Q Consider the boundary value problem defined by the partial differentia equation in x t 8 6 2 6 x x y and the conditions Let o x y 8 6...
- Q Save ularity The quartic function f x 0 002x 4 0 025x 3 0 364x 2 7 243x 86 993 d to estimate the number of dolls of this type...
- Q Which of the following functions there may be more than one are solutions of the differential equation y 4y 4y et Oy e t Oy et y te t et...
- Q question below Graph the circle with equation x 2 y 2 25 Plot the center and then a point on the circle 6 5 4 3 2 Clear AIL Draw...
- Q In the diagram below QN NP 2 3 and QP 10 Find the radius of 0 P 13 Q2 R 14 S Enter a number only
- Q Find d y dx d y dx in terms of x and y x y 10x 2 3x 14 10xy 2 25 4 2 x y X
- Q COOOOOOD similar polygons scale factors dilation enlargement reduction isometry right triangle legs of right triangle hypotenuse QPythagorean Theorem angle of elevation depression trigonometric ratio sine cosine tangent identity The polygons...
- Q Determine a region of the xy plane for which the given differential equation would have a unique solution whose graph passes through a point xo yo in the region G...
- Q a Fill in the blanks with the coefficient f x x6x4 2 x 1 x 1 CO C1 C2 Hint Use Taylor s Theorem to find the Taylor series of...
- Q 3 Find and classify the equilibrium solutions for the each of of the following differentia equations a y 3 y b y 5 y c y y 3 y d...
- Q Find the eigenvalues and eigenfunctions for the following boundary value problem with 0 y xy 0 with y 0 0 y 5 0 Eigenvalues An 22 2n 1 100 Eigenfunctions...
- Q 3 In the apothecary weight system one scruple is 20 grains and three scruples equals one dram Determine the number of grains in 50 drams 4 On a trip of...
- Q The limit below represents f c for some function f and real number c 8 x 16 2 x 8 Determine the function f lim I 8 f x Determine...
- Q Suppose f x is continuous over an interval a x b and a c d b If f c 5 then check all that apply f x is increasing through...
- Q tempt 1 0 5 points eing dumped from a conveyor belt at a rate o is such that it forms a pile in the shape of a d are always...
- Q Determine whether 31 is a solution of the le 31 a solution
- Q 0 Suppose a population of rabbits Y is given by the logistic equation 300 5 55e 84t y where Y is the number of rabbits at time t in months...
- Q 13 15 SIX 213 17 5 5 2x 1 x x 12 x 9 Rationalize the numerator b a b a 14 2 x 3 18 1 16 x hx...
- Q Find A the area of the region under the curve y 2x 9 and above the x axis for 2 x 5
- Q For the data provided below what is the median 1 3 5 6 6 7 9 10 14 14 15 16 20 21 27 32 41 O 14 01 O...
- Q 20 points Linearize the following nonlinear differential equations for the input equilib rium of u 1
- Q Product Quotient and Trig Let f x and g x be differentiable functions such that f 5 2 f 5 6 g 5 4 and g 5 3 If h...
- Q 6x y 9 and passing through 6 7 Express the equation in standard form
- Q The region R in the first quadrant of the zy plane is bounded by the curves y x 0 and y 0 A solid S is formed by rotating R...
- Q A bucket filled with sand has a total weight of 25 pounds You begin steadily lifting the bucket to the top of a building 35 feet above the ground using...
- Q f x is the horizontal axis is X Given the differential equation x t f x t List the constant or equilibrium solutions to this differential equation in increasing order...
- Q A trough full of water is 7 meters long 2 meters wide at the top and 2 meters deep with vertical cross sections parallel to the ends shaped like an...
- Q 3 Find each solution x t determine any stable equilibrium solutions a x 5x x b x 2 x
- Q Knowledge check 1 winter 2U23 2 1 par a On what interval Aa 8 EB February 4 2023 at 1 19 PM on what intervals would the graph of your...
- Q A cliff diver leaps from a 100 foot cliff into the Pacific The diver s height above the water is modeled by the function P x 16x 2 10x 100...
- Q Rain water flows into an open tank at a rate of g t 200e 0 3t where g is in gallons per day and t is in days The water...
- Q The contour plot of z f x y is shown below Determine if the given quantity in each part is positive negative or zero Negative V 1 Negative af x...
- Q A particle moves along a line At time t in seconds the particle s velocity is v t t 6t 8 in m s Find the particle s net displacement...
- Q Let f f x dx 7 a What is the average value of f x on the interval from x 0 to x 4 average value b If f x...
- Q Given D 2 3 2 1 D 2 3D H 0 where I 1 0 0 1 find the value of k
- Q Use the Laplace transform to solve the following initial value problem y 4y 32y 8 1 2 y t y 0 0 y 0 0 Notation write u t c...
- Q Find the area of the surface generated by revolving the given curve about the x axi y 4 x 1sxsl
- Q Find the indicated functional values f x 3x 3 2x 2 3x 4
- Q a b Find the exact numerical value of each expression sinh ln3 cosh In 2
- Q List out all possible numerators of the rational roots of the function g x 2x 5 4x 4 8x 3 2x 2 x 8 Use commas to separate
- Q ple gives the increase or decrease in the number of donors to a college athletics support organization for selected years Rate of Change of Donors to a College Athletics Support...
- Q According to the 68 95 99 7 Rule 99 7 of high school seniors had SAT scores between what and what
- Q 1 Vertex Domain 0 9 8 Range 0 118 Axis of Symmetry x 5 Zeros Y Intercept Average rate of change between second 1 and second 3 The Average rate...
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