Compare and discuss the long-run behaviors of the function below. Enter the constant or the polynomial that the rational function behaves like as x→±∞: h(x)=(x⁴+9)/(x³+8)

Q: 2. Approximate the value of f(x) = √√3+ x2 at x = .9 using the linearization process.

A: The linearization of the given function is:L(x)=21​x+23​ The approximate value of the function at x…

Q: Explain the difference between an absolute minimum and a local minimum. ○ A function f has an…

A: The final solution is:"A function f has an absolute minimum at x=c if f(c) is the smallest function…

Q: (3) (LATEX question) Let n = N and take any cЄ R. Find lim x c xn- cn X - C

A: Let .To find the following limit.

Q: U² - 2 If y = sin U+2 and u = cos(x² +2x+1), find- ddy dx dx Note: Just do the single derivative and…

A: The single derivative is:dxdy​=−sin(x2+2x+1)⋅(2x+2)⋅cos(u+2u2−2​)⋅((u+2)2u2+4u+2​)The value of dxdy​…

Q: if f(x)=16x+3 find f prime of zero

A: The objective of the question is to find the derivative of the function f(x) = 16x + 3 at the point…

Q: 1. f(x) = (4 — x²)5

A: Second derivative test for local maxima and minima :

Q: find the x intercepts y intercepts of (x−3)(x−1)(x+4) (x−2)(x−5)

A: The objective of the question is to find the x-intercepts and y-intercepts of the given function…

Q: Evaluate the definite integral. 5 L³× √5x² - 4 dx X

A: Answer is  3266​Explanation:Step 1: Step 2: Step 3: Step 4:

Q: Let z(x, y) = √√x² – y² + 25. Graph the boundary of the domain of z below and indicate whether the…

A: Given :-z(x,y) = Now, z(x,y)  0So,  = 0-x2 - y2 + 25  0x2 + y2 25Now drawing the graph i.e.,

Q: We begin by finding the EL equation for the auxiliary functional S[y] = = - S₁ 12 dx (xy2+ Ay - λy)…

A: Please see the attached image for an explanation. Thanks.Explanation:

Q: The graph of the derivative f' of a function f is shown. y=f'(x) (a) On what intervals is f…

A:

Q: 1. Find the value of the expression lim x²+x+21 X-3 x-1

A:

Q: (4/x3 + 1) dx

A:

Q: 3. f(x) = (x - 1)² x2+1

A: The given function

Q: For which values of t is the curve concave upward? (Enter your answer using interval notation.)

A: To find the values of  for which the curve is concave upward.

Q: (9x8 - 2x - 6) dx

A: The given integral is

Q: 1 L²x √ x² 0 x√√x²+1dx

A: I=∫01xx2+1dx

Q: 1.18. Evaluate the sums: n Σκ2 k=1

A: To evaluate the following sum.

Q: When the velocity v of an object is very large, the magnitude of the force due to air resistance is…

A: Shell of mass = 3kgInitial velocity = 800m/secMagnitude of the force due to air resistance is…

Q: Calculate y dx (25th derivative) of y = sin.x. It may help to first determine a pattern. Paragraph V…

A: The objective of this question is to find the 25th derivative of the function y = sin(x). To do…

Q: PLS ENSURE YOU GET RIGHT ANSWER AND DOUBLE CHECK AND Solve this based on only contexts from Natural…

A: dx25d25y​=sin(225π​+x)=cosxExplanation:Step 1:we have y=sinxdifferentiate…

Q: Find the interest rate needed for an investment of $4000 to grow to an amount of $8500 in 4 years if…

A: To find the interest rate needed for an investment of $4000 to grow to anamount of $8500 in 4 years…

Q: Let s(t)=4t to the thrid power+30t squared+72t be the equation of motion for a particle. Find a…

A: Part(a) :  v(t) = 12t2+60t+72 Part(b) :  t = -3 and t = -2 Part(c) :  a(t) = 24t+ 60Explanation:

Q: Sketch the graph of the function by making a table of values. Use a calculator if necessary.…

A: given function h(x) = (1.3)x

Q: Assignment 10: Problem 7

A: 12Explanation:To find the minimum value of the function f(x, y) = x² + y² subject to the constraint…

Q: Given that y COS X, find d83y dx 83 It I may help to first determine a pattern.

A:

Q: M8 n=T 3-sinn n M

A:

Q: The region W lies between the spheres x² + y²+z2: 24 and ²+ y²+ z² == I' 16 and within the cone z =…

A:

Q: 3. Use the Chain Rule to find the indicated partial derivatives. (a) w = x² + y² + z², x = st, y = s…

A: Note- As per company guidelines for multiple questions posted we are allowed to solve only one…

Q: You can see that the amount of medication enters the therapeutic window quickly, but goes below the…

A: Solution is given below Explanation:Step 1: Step 2: Step 3: Step 4:

Q: The points A[−1, 1, 1], B[2, 0,3], and C[3, 3, -4]. Show that this triangle is a right-angle…

A: Please see the explanation Explanation:Step 1:

Q: Consider the equation below. (If an answer does not exist, enter DNE.) f(x) = e⁹x + e-x (a) Find the…

A: Given: To Find: (a) To find the intervals on which f is increasing and decreasing.(b) To find the…

Q: If sin x = 4 , x in quadrant I, then find (without finding x) sin(2x) = cos(2x) = 5 Enter a…

A:

Q: Hello, I am currently stuck on this problem in the alternating series section of series and…

A: The problem involves analyzing an alternating series, given by the equation:[ \sum_{n=1}^{\infty}…

Q: (b) Find parametric equations that represent the line segment from (-1, 7) to (1, 3) for 0 ≤t≤ 1.…

A:

Q: Ar x+4x²+5x+2 x+1 x2 x+2

A: solving the given equation

Q: PLS ENSURE ITS RIGHT ANSWER AND DOUBLE CHECK AND Solve this based on only contexts from Natural…

A: f′′(x)=16sec2(x−2)tan2(x−2)+8sec4(x−2)Explanation:Given function isf(x)=4tan2(x−2) Step…

Q: Suppose f(x, y) = x² + y² + x²y + 6 and D = {(x, y) : |x| ≤ 1, |y| ≤ 1}. Answer the following

A: The given function is

Q: Evaluate the line integral [ z²dx + x²dy + y²dz, where C is the line segment from (−1, −1, −1) to…

A: We have line integral(Z2dx+X2dy+Y2dz) Over curve C Where C is the line segment from (-1,-1,-1) to…

Q: Ex 2. i) Determine whether the Mean Value Theorem applies to the function f(x) = 7-x² on the…

A: f(x)= 7-x2We have to check for M.V.T theorem and also find the values

Q: Calculate the area of the parallelogram whose adjacent sides are: a = [5,3,-1] and b = [2, −4,1]

A: Therefore, the area of the parallelogram formed by the vectors (a)  and (b) is  27.08 square…

Q: Calculate the volume under the elliptic paraboloid z = x² + 3y² and over the rectangle R = [-3,3] x…

A:

Q: Find the area of inside = 22cose and outside = 11 by sketching the graph of the equations using the…

A: Option B is correct.Explanation:Graph. If you have any problem let me know here in comment box for…

Q: iven f(x,y)=- use differentials or a linear approximation to approximate the value of y' +1 f(1.01,…

A: The given function is

Q: Water is leaking out of an inverted conical tank at a rate of 12500 cubic centimeters per min at the…

A:

Q: For the following vector, convert from magnitude and direction to x and y coordinates r = 6,0 = 350°…

A: x = 5.91 y = -1.04Explanation:Approach to solving the question:Detailed explanation:Please see…

Q: Find the critical numbers of the function f(x)=-12x to the fifth power  - 75x to the fourth power +…

A: The objective of this question is to find the critical numbers of the given function and classify…

Q: 3(x+2)+2 for 3 1 Use the given formula to answer the following questions. (a) For each of the values…

A: I gave a detailed explanation of each parts in the below steps.Explanation:Step 1:Step 2:Step 3:Step…

Q: find the equation of the line tangent to g(x)=x^2+x at (2,6).

A: Find the equation of tangent to  at

Q: A result is called "statistically significant" whenever a. The null hypothesis is true b. The…

A: The objective of the question is to identify the correct condition under which a result is…