The derivative of h(y) = (2y² − 3y)˚(y + 6)² requires the product rule and is given by h'(y) = (2y² − 3y)³(2(y + 6)) + (5 (2y² − 3y) ¹ (4y − 3)) (y + 6)² - - Factor the derivative of f. h' (y)

Q: Two measurements are given. Find the absolute difference and then find the relative difference as a…

A:

Q: Find u v, uu, ||u||2, (u v)v, and u. (2v). u = , V = (a) u. V 27 (b) 306 (c) 306 (d) (e) u u ||u||²…

A:

Q: ·Sex tan² (ex) dx 3 .fx cos ³ (x²) dx

A:

Q: Find the general solution of the differential equation. 16y(4) y(x) = = y

A:

Q: 26. Find a vector perpendicular to both a = [1, 2, 3] and 5 = [3, 2, -1].

A:

Q: P(t) = 0.01484t2 + 0.446t + 15    (0 ≤ t ≤ 22) where t is measured in years, gives the percentage of…

A: We have given,   P(t) = 0.01484t2 + 0.446t + 15    (0 ≤ t ≤ 22)

Q: Suppose f(x) = cos x. Without using the AROC formula or a calculator, find the average rate of…

A:

Q: Determine whether the relation is a function. Give the domain and the range of the relation.…

A: Given that the relation is a function to find the domain and range

Q: 16. y' = (1 − y) cos x, y(t) = 2

A:

Q: I sin¹¹1 x cos³ x dx

A:

Q: Sketch the level curves of f(x, y) = y + 2x r² +3 at k = 0, 1 on a common Cartesian plane.

A:

Q: Parameterize the curve of intersection of the surfaces so that the direction is clockwise when…

A:

Q: Complete the following problems applying the Intermediate Value Theorem, when applicable. Complete…

A: (1) By applying the IVT to determine whether  has a solution in one of the intervals .(2) For . To…

Q: I. Solve each system of equations using SUBSTITUTION METHOD {v=52 1. 5x - y = 6 2x²-3x + 2

A: To solve the following system of equations by using the substitution method.Note: Since the student…

Q: 2. Sketch the graph of the piecewise defined function x² for x 0 Evaluate f(5), f(0), f (-3). g(x)…

A:

Q: 18. If three planes intersect in a point then the triple scalar product of their normal 19. In…

A: Statements are given.18. If three planes intersect in a point then the triple scalar product of…

Q: 4. Without using L'Hôpital's rule, evaluate the following limits. Furthermore, if the limit does not…

A: To find:-(a) (b) (c)

Q: Find the indicated derivative. dx dy dx = for y = x14

A:

Q: Write the system of equations associated with the following augmented matrix. 105 0 16 The system of…

A: Consider the augmented matrix

Q: Analyze the function below. Which of the following is/are true? 8 f (d) 81 82 8 x+5 as x→ 1+, f (x)…

A:

Q: The Seventh Gate As you approach the seventh gate, you notice that it is only a short distance to…

A: Given:: f(x)=√(2-58x)Find domain of f'(x).Since,d(√x)/dx=1/2√xTherefore,f'(x)=1/2√(2-58x) .…

Q: St tan³ x secx dx

A: since you have posted multiple questions in this question which are not interlinked so i have solved…

Q: Indicate if the zeros are significant in each of the following measurements. Drag the appropriate…

A: The given measurementsAs we know leading zeros (zeros to the left of the first non zero digit) are…

Q: I am planning a snack package of fruit and nuts. Each ounce of fruit will supply zero units of​…

A:

Q: Find the local linear approximation of the function f(x) = √4+xatxo = 0, and use it to approximate…

A:

Q: Parameterize the portion of the surface f(x, y) = xy in the first octant, bounded by the planes x =…

A: We have to parametrize the portion of the given surface.

Q: Let f be the function satisfying f'(x) = 2x – 3x f(x) for all real numbers x, with f(0) = and lim…

A:

Q: Set up a system of linear equations to represent the scenario. Solve the system by using Gaussian…

A:

Q: If f(x) = (3x + 7)−², find f'(x). Write your answer using negative exponents. Find f' (3). Write…

A:

Q: The current population of a certain bacteria is 5687 organisms. It is believed that bacteria's…

A:

Q: Construct a truth table and determine whether the given compound proposition is a tautology,…

A:

Q: X a) y = x²-1 x-1

A:

Q: Find the general solution of the differential equation. (4) 256y+) = 16y

A: Given that :-256y(4) = 16yWe find the general solutions of this given differential equation.

Q: Find the intercepts of the plane 2x+6y3z- 12 = 0

A:

Q: f(t) = 4t2;    t = 5, t = 5 + h (a) Determine the net change between the given values of the…

A: The function is f(t)=4t2 (a) The aim is to find the net change at t=5 to t=5+h

Q: 24. By analysing the normals, determine if the two planes intersect in a line, are parallel and…

A: If  is the angle between the planes  then

Q: Which of the following vectors is perpendicular to i? i+j i-j i - 2j -2i -2j None of the above

A:

Q: The graph of a function f is shown below and describes the position of a particle as it moves along…

A:

Q: Suppose the total cost of producing q units of some commodity is given Gla) 0.001² -

A:

Q: Express this function as a power series. (Use power series representation of functions.) 2 + 10x 3-…

A:

Q: 1 Let F(t) = (vt - 4, 4e², ²3). t-3 12 [1² F(t)dt = { Evaluate the definite integral.

A:

Q: In 1980 the population of alligators in a particular region was estimated to be 1600. In 2007 the…

A: given that population in 1980 is 1600, whereas population in 2007 is 6500.t=2007-1980=27 years

Q: (a) Write an equation for a graph obtained by vertically stretching the graph of y = x² by a factor…

A: The given parent function is

Q: -3 A curve has for its third derivative equals to x If (1, -1) is a point of inflection of " the…

A:

Q: Order 7 of the following sentences so that they form a proof for the following statment: Choose from…

A:

Q: If f(x) = 4x² 6x + 3, find f'(3). Use this to find the equation of the tangent line to the parabola…

A:

Q: Cathy wants to determine the height of a Flag pole shown below. She uses a survey instruace to…

A: The figure

Q: 4. y' - 2xy = ex²

A:

Q: 28. Determine the point of intersection between the following pair of lines r = (5, 1, 7) +…

A:

Q: Evaluate the integral. (Use C for the constant of integration.) [(1 + √/sin(t)) cos³(t) dt

A: