Determine all the relative minimum and maximum valucs, and saddle points of the function h defined by h(x, y) = x* – 3x + 3xy?.

Q: Which of the following correctly describes the function f(x) = 4x4 – 32x³ + 89x2 – 95x +29? none of…

A: This is a problem related to function. Based on the graph of the given function we will answer the…

Q: S (e7z +8) dæ

A: LetI=∫ (e7x+8)dxWe apply the Sum RuleI=∫ e7xdx+∫ 8dxI= e7xddx(7x)+ 8xdx+CI=17e7x+8x+C∫…

Q: Evaluate the summation 4i + 4. i=1 140 116 224

A:

Q: Find the general solution of the following differential equations: a. +6- dr + 9 0. dr3 dr² dy + 4.…

A:

Q: The temperature is T degrees at any point (x, y, z) in three-dimensional space and T(x,y, z) = 1/(x²…

A: Here, the temperature is given by: T(x,y,z)=1x2+y2+z2+3 Now,…

Q: The dimension of the vector space P3 is equal to: Select one: O 5 none of the others O 2 4 O 3 ):…

A:

Q: Evaluate the integral of F(x,y) = x^2 y^3 in the rectangle with vertices (5,0);(7,0);(7,1);(5,1)…

A: We have to evaluate the integral of F(x, y).

Q: J sech(5x+1)tanh(5x+1)dx

A: Topic:- application of integration

Q: Find the area under the graph of the function over the interval given. 13) y =ex; [-9,4] A) e 13 B)…

A: We can find the area as below.

Q: Let C(x) be the cost, in dollars, to produce x gallons of gelato. What is the meaning of C'(5) = 4.5…

A: Given, C(x) is the cost in dollars. x is the gallons of gelato.

Q: vector v is multiplied by the scalar -, the resulting vectór 4' smaller than v and in the same…

A:

Q: Use the numeric integration feature on your calculator to find the integral. 4. 27) A) 0.88623 B)…

A: We can find the answer as below.

Q: 1 g(x, y) = cos (Tx VT) + log3(x – y)' Calculate the instantaneous rate of change of g at the point…

A: To solve the following problem

Q: if x >0 if x = 0. Find f' (0) using the definition of derivatives. sin 4x 3. Suppose f(r) = {0 x* +…

A:

Q: y" + 3y' + 2.25y = 91' + 64, y(0) = 1, y'(0) = 31.5

A:

Q: Both pictures are same question!

A: Given radius=8  and angle is 65° we need to find the area of the sector A The area of the sector of…

Q: Calculate the left rectangle approximation of 3x- dx using five subintervals.

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Q: Find the following for the vectors u = 6i – 5j + 7k and v = - 6i + 5j - 7 k. a. v•u, v|, and u b.…

A:

Q: Lagrange Multipliers will be used in order to solve the following: Maximize f(x, y, z) = 4x + 2y + z…

A: We want  to maximize the function.

Q: 50 ee the wWind, a plane would fly due east at a rate of 150 mph. The wind is blowing southeast at a…

A:

Q: Find the interval of convergence of the series. Sn=00 (z-8)" n=1 n+8 O -1 < x < 1 O - <z < -00 <x<…

A: We ahve to find the interval of convergence of the series.…

Q: x = 3 is a critical number of the function f(x) = (x+ 3)(x - 3)2. Select one: True O False

A:

Q: Calculate the test-statistic, t with the following information. ni 20, ãi 2.37, s1 0.3 %3D n2 = 30,…

A: We have to find the test statistics.

Q: 21) y" – 2y' +10y = 0, y(0) = 3, y'(0) = 3.

A:

Q: Find the average value of the function f(x)= e²x on the interval [0,4]. O a. 372.5 O b. 1490 O c.…

A: Topic = Application of integration

Q: Find the derivative of h(x) = sin2x

A:

Q: Evaluate ds, where C is the path defined by c(t) = (t², 9t, 4t³3/2) where 0 <t < 2.

A: Given integral c z^2/x ds, C(t) =(t^2, 9t, 4t^3/2)  where 0&lt;= t&lt;=2

Q: On a map, Orlando is 178 mm due south of Niagara Falls, Denver is 273 mm from Orlando, and Denver is…

A: Explained below

Q: Calculate the left rectangle approximation of - using five subintervals. dx L5 = 1.260 O L5 = 0.746…

A:

Q: Consider the function f (z) = es: Show that if f (z)is purely imaginary, then 2n +1 T, n = 0,±1,±2,…

A: Complex function

Q: Find the Taylor polynomial of order 3 generated by f at a. f(x) = x? + x + 1, a = 5 O P3(x) = 1 +…

A:

Q: s-3 F(s) = The inverse Laplace Transform of is O f() = sin 3t – 3 cos /3t %3D O f() = /3 sin /3t-3…

A:

Q: 32

A: We need to use the knowledge of binomial theorem to solve this problem.

Q: Use Lagrange Multipliers to solve the following: Maximize f(x, y, z) = 4.x + 2y + z subject to x +…

A: Apply Lagrange multiplier

Q: For the list of degrees below: degree Ahmed 66 name Ali 90 Mona 45 Salma 76 Karim 78 Use…

A: As per our guidelines we are supposed to answer only 3 sub-parts. Kindly repost others. Thank you…

Q: An object is being heated such that the rate of change of the temperature T in degree Celsius with…

A: Here we have to use the Runge-Kutta 4th order method

Q: af Given the function f(x,y,z) = x cos z +x*y*e" , determine dz

A:

Q: Let U be the universal set of natural numbers less than 11. Consider the following two sets. A = {2,…

A:

Q: 7x +4 1+1 if I1 1. Evaluate f(-3) (A) –17 (C) 11 (B) 10 (D) undefined 2. Evaluate f – 2() (A) –10…

A: Topic:- function

Q: Use the Alternating Series Test to determine whether the alternating series converges or diverges.…

A:

Q: Evaluate the following limits or explain why the limit does not exist lim as x approaches 0…

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Q: 3x2 dx . 4. Evaluate 7x +C 3/1-x cos (3x) + C sin-1(x³) + C The antiderivative cannot be found

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Q: Use the Euler , improved Euler and Runge-kutta nethoods to solve the following ODES : y - y tan x =…

A:

Q: 4x2-3 f (x) 2х3+x2+7

A: Explanation of the answer is as follows

Q: (b) Find the values of a and b so that the function = x + ax + b has a local maximum at the point…

A: topic - application of derivatives

Q: 4. -1 y%3D 3x-9

A:

Q: +)Use the Runge-Kutta Method SeVelue:.

A: Given y′=(1+1/x)⋅y,y(1)=2.7183,h=0.2,

Q: 1 dy J yi + 3y² + 1

A:

Q: Find the volume of the solid in R' bounded by y = x2, x = y?, z = x + y + 27, and z = 0.

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Q: Write each of the other trigonometric functions of e in terms of cos(e). (En sin(e) = V1- cos (0)…

A: P