5) (10 ptos) Determine los puntos críticos de ƒ(x) = ²x³ + x² – 2 2x

Q: Q2. If F = (x² - y² + 2xz)ī− (2xz − xy + yz)j + (z² + x²), find the divergence of curl F and curl of…

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Q: Let f and g be functions satisfying that f(1) = 3, g(1) = 4, f'(1) = 1, g'(1) = 5. For the following…

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Q: Solve the following differential equation by using the Laplace transform techniques. d²x +8- dt² dx…

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Q: Calculate the derivatives (f(g(x)))' and (g(f(x)))' if f(x) = x² g(x) = 1 8x + 1 (Express numbers in…

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Q: question, show all steps so I can understand the problem Use the following property of the definite…

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Q: Compute the dot product of the vectors v and w, and find the angle between the vectors. v=5i-j and…

A: We have to find the dot product of vectors and magnitude of vectors

Q: Show that the vectors , and are coplanar.

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Q: The half-life of a certain substance is 3.6 days. How long will it take for 20 g of the substance to…

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Q: Find all values of c such that fis continuous on (--,-). f(x) = {7-2², c=2.193 c= 3.193 7-2²³, xse…

A: The given function,    fx=7-x2,x≤cx,x>c

Q: ht plane to th t the point where (x, y) = (2, 2) has the equation z = ƒ (x, y) = ln (4x4 y+1) OSP

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Q: Consider the implicit function. e' = sin (6x) Determine the formula for in terms of x. dy dx

A: Here we have to find the derivative.

Q: Two bacteria cultures are being studied in a lab. At the start, bacteria A had a population of 60…

A: Topic:- exponential growth function

Q: In Problems 13-16, graph the constant-cost lines through (9, 9) and (12, 12). Use a straightedge to…

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Q: ich of the following is a power series representation of f(x) = f(x) = Σ(-1)" – n=0 x2n+1 f(x) =…

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Q: Given the same three points P (1, 4, 6), Q (-2, 5, -1)  and R (1,  -1, 1).  Find a vector equation…

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Q: Find the x-values (if any) at which is not continuous. Which of the discontinuities are removable?…

A: topic- limits and continuity

Q: Determine whether the following series converges or diverges. n² +1 Σ n² +n +8 n=2

A: We have to find the series is Convergent or divergent.  We can apply limit rule to check it.

Q: Find a particular solution to the differential equation Ур || y" + 5y' + 6y=-108t³.

A: Given differential equation is y''+5y'+6y=-108t3 We have to find a particular solution for it.

Q: A spring is stretched 6 in by a mass that weighs 8 lb. The mass is attached to a dashpot mechanism…

A: Given :The spring is stretched 6 in by a mass that weighs 8 lband damping constant…

Q: b) [. obtained curve 1: Find the volume of the solid by rotating the region bounded by the y = -x² +…

A: Solve the following

Q: In a triangle ABC, points E and F are on the sides AC and BC respectively, such that AE is 1/3 of AC…

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Q: Determine the following indefinite integral. S ex 400-e2x dx, x> In 20

A: Given, ∫ex400-e2xdx

Q: After receiving his first income, Mr. J invested P20,000 in a bank for his future family. The annual…

A: This question can be solved by applying the concept of compound interest.

Q: Consider the function g(x) =−4 log (−1/3 (x + 2)) + 1. a) Describe, in order and with detail, the…

A: We will use concepts of translation , dilation and reflection.

Q: The series is divergent. Select one: O True O False Σn=1 4n³ + 4 5 5 7 n° +1

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Q: Find the critical points of the function f(x, y) = y² − x² + - a. [ b. I function f(x, y) = Find the…

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Q: Parameterize the plane that contains the three points (-2,-2,-2), (-12, 2, 12), and (0, 35, 30).…

A: To find the parametric equation of a plane containing three points (-2,-2,-2,), (-12,2,12) &…

Q: Suppose that a particle moves along a straight line with velocity v(t) = 7 - 3t, where 0 ≤ t ≤ 0.5…

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Q: You are making a rectangular box with a square base. Its volume must be 8 ft^3 . Find the dimensions…

A: A rectangular box with a square base. Its volume must be 8 ft3

Q: Let f(x) be defined by f(x) = x² sin(x) + x³. Find f'(1). Note: Your answer (if it's not an integer)…

A: Please see the below picture for detailed solution.

Q: A tank contains 40 gal brine for which the concentration is initially 3 lb/gal of salt. A brine…

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Q: Find the marginal profit function if cost and revenue are given by C(x)= 185 +0.3x and R(x) = 3x…

A: Recall: Profit, P(x)=Revenue-Cost Marginal profit=P'(x) We have, R(x)=3x-0.02x2, C(x)=185+0.3x

Q: Determine the Laplace Transform of the following functions: a. f(t) = 3te-5t cos(2t) b. g(t) = f(27)…

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Q: Let f(x) be defined by Find f'(1). f(x) = (2x - 1).

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Q: Find the gradient of the function z(x, y) at the given point P: z = cos(x² + y²), P(3, — 4).

A: The given function is z=cos(x2+y2), P(3,-4).

Q: II) Let f be the piecewise function f(x) = x³ + 6x² + 8x x+2 1-x-2, -, x≤-1, x -2 -1 1 1) Sketch the…

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Q: 9. (a) Express 2 x4 – x² as partial fractions. (b) Hence, compute the exact value of the following…

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Q: Determine the following indefinite integral. S dx x√√81-x 18

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Q: Exercise 4.4.5 A thin plate lies in the region between y=x and the x-axis between x = 1 and x=2.…

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Q: g(x) = cos ¹x+ x 1-x²

A: Topic = Derivative

Q: A car depreciates by 17% each year. The value of a $30 000 over time is modelled by the function v =…

A: The given data is: The value of a $30,000 over time is modeled by the function v=300000.83t To find:…

Q: i) Find the general term (an) of the sequence 3e-²,4e¯4,5e¯6,6e-8, 7e-10, 8e-¹2,... ii) Calculate…

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Q: Question 1 [ Use the method of Lagrange multipliers to find the extreme value(s) of f(x, y) = xy…

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Q: Calculate the accumulated amount of end-of-month payments of $9,000 made at 5.89% compounded…

A: The given data is: Monthly payement=$9,000Interest rare r=5.89%=0.0589Time t=5 years  Compounded…

Q: Grandma wants to give you $540 at the beginning of each month while you are at school for 3 years.…

A: We know that, Future value = PMT × p {[(1 + r/n)(nt) - 1] / (r/n)} where, PMT is the periodic…

Q: Find the center, vertices, and foci of the ellipse 4x² + y²-8x+4y-8=0.

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Q: solve the differential equation dy/dx=2x^4sqrt of y, y.0

A: Solution of given question is written in below steps.

Q: Find an equation or inequality that describes the following object. A sphere with center (4,1,1) and…

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Q: Find the distance of the point (2, 6, 4)  from the x-axis by two methods

A: To find the distance between the point.

Q: Use a double integral to find the area of the shaded region. -3 -1 π/2 -3 r = 2 cos 20 3

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