f(x) = x²(x

Q: Consider the function f(x) = x² - 6x +8 x-1 a. Find the first derivative. f'(x) = b. List any…

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Q: Solve y'' + 4y' + 4y = 0, y(0) = 3, y'(0) = y(t) = 9

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Q: Find the value of the logarithm. (1) In

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Q: If x is divisible by 5 or y is divisible by 5, then xy is divisible by 5.

A: Let x is divisible by 5. Then x=5u for some natural number u.

Q: Question Use the trapezoidal rule to calculate the absolute error of ¹(5x³ + 5x) dx using 3…

A: I am going to solve the problem by using some simple calculus to get the required result of the…

Q: Use Euler's method with step size 0.5 to compute the approximate y-values y1, y2, y3 and y4 of the…

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Q: A function and its graph are given. Use the graph to find each of the following, if they exist. Then…

A: Note: Since the student has posted many sub-parts of the question and does not mention any specific…

Q: Find an nth degree polynomial function with real coefficients satisfying the given conditions n=4…

A: Given query is to find the function.

Q: The city of Anville is currently home to 26000 people, and the population has been growing at a…

A: We are authorized to answer one question at a time,  So we are answering the first one, please…

Q: Consider the function f(x) = x³ - x¹ + ?x³ + ¾x + 20 (a) Find where the function is concave up. + ¾.

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Q: Exercise 8 Form the difference quotient lim h→0 Exercise 9 f(x+h)-f(x) h Evaluate the limit lim (x².…

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Q: Find each limit, if possible. (If an answer does not exist, enter DNE.) 7x +5 (a) lim (b) lim (c)…

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Q: 2. Sketch the domain of the following functions: a) f(x, y) = b) f(x, y, z)= 2-x-y - eª %2 In(4-x² -…

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Q: Use Simpson's Rule with n = 10 to estimate the arc length of the curve. Compare your answer with the…

A: Here we have to use the Simpson's rule.

Q: 2²u u Verify that the following function satisfies Laplace's equation, + ax² ay² u(x,y) = 7y (3x² -…

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Q: 4. The marginal profit from making and selling x products per day is P'(x) = 350 + 4x - 3x² Find the…

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Q: Find all the local maxima, local minima, and saddle points of the function. f(x,y)=√56x²-9y²-16x-31…

A: The function is given as , fx,y=56x2-9y2-16x-31+1-8x find the local minima , local maxima and saddle…

Q: Pick any three vectors u, u, and w (e.g., u = (2,-1,2), = (-3, 4, 0), = (1, 3, 2)). Determine the…

A: Givenu→=2,-1,2=2i^-j^+2k^v→=-3,4,0=-3i^+4j^+0k^w→=1,3,2=i^+3j^+2k^

Q: 1. Integrate each of the following. a. f 3x²e³x dx b. fxco. xcos(4x)dx

A: (a) Given that ∫3x2e3xdx

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Q: Exercise 6 Limits The following graph of the function f satisfies lim f(x) = 2 . For & = 1.5 find a…

A: Given that limx→3f(x)=2  and ε=1.5

Q: Let f(x) = f'(x) = = 4 cos x + 5 tan a ƒ' ( − 7 ) = = Question Help Video Morrago instructor (round…

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Q: Question Determine which of the following tests would be best to use to determine the convergence of…

A: Solution: ∑n=1∞9n37 Apply p series test if the series is of the form  ∑n=1∞1np, where p>0 If…

Q: If x is even, then 7x + 9 is odd.

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Q: Solve the given differential equation. y" + 4y = 12y' The values c₁ and c₂ are arbitrary constants.…

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Q: Cost, revenue, and profit are in dollars and x is the number of units. Suppose that the total…

A: Given query is to find profit and marginal profit.

Q: Differentiate the given function using the appropriate rule(s). Your answer does not have to be.…

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Q: 3. The limits below do not exist. Verify this by showing two different pathways that result in…

A: as per company guidelines we solve only first question when multiple question being posted.

Q: The rate of growth dP/ dt of a population of bacteria is proportional to the square root of t, where…

A: Given query is to find the population after 6 days.

Q: 1. Evaluate the following definite integrals using the Fundamental The- orem of Calculus (b)+12+ dr

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Q: Write an equation for a rational function with: Vertical asymptotes at x = -2 and x = -4 x…

A: Here vertical asymptotes at x = -2 and x = -4 we have denominator (x+2) and (x+4) as co-factor .…

Q: 5. Given 20 different types of inputs to a program, in how many ways can 8 of them be selected if…

A: Topic -Permutation and combinations When order matters in selection, we use permutations . When…

Q: Consider the following function. g(x) = 3x³ - 8x Find the first and second derivatives of the…

A: Consider the following function.gx=3x3-8xTo find the first and second derivatives of the function.To…

Q: If f(x) = 7 sin x + 10 cos x, then f'(x) = f'(3) = (round to 3 decimal places)

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Q: I dont understand what is written. Can you write in another way or atleast have spaces in between…

A: Here we have to determine the sum of convergent series.

Q: y²dx + (3xy + y² - 1)dy = 0 ex + ln y + ²) + 2) dx + dx + ( + lnx + siny) dy = 0

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Q: Solve the equation 9x cubed + 9x squared - x - 1=0 govem tjat -1/3 is a zero of f(x)=9x cubed + 9x…

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Q: The following graph of the function f satisfies limf(x) = 2 . For = 3 find a value of 8>0 such that…

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Q: Does the graph of the function below have any horizontal tangents in the interval 0≤x≤2r? If so,…

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Q: The graph of the function f(x) = x³ is translated horizontally to create g(x). If the point (4, 8)…

A: We can solve this as follows:

Q: If f(x) = x cosh 1 يع امت - √x² 9

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Q: 4. Let f(x)=2x4-5x² + 2x sin(x) *20 x < 0 (a) Prove f(x) is continuous everywhere. (b) Prove there…

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Q: Find an equation of the tangent plane to the surface at the given point. y (1, 9, 9) f(x, y) = −9x +…

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Q: i need help with, b, c and d

A: Part b: A horizontal asymptote of a graph is a horizontal line y=b if the graph approaches the…

Q: Find the first and second derivates of the functions. h(t) = t^4 - 7t^3 + 5t^2 - 8t - 14…

A: Find the first and second derivative of the function

Q: lim (1+1)* 148

A: Please see the below picture for detailed solution.

Q: Let g(x) = f f(t) dt, where f is the function whose graph is shown. Answer the following questions…

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Q: Question Use the method of partial fractions to evaluate the following integral. √ 23 ²2 64 da dx x3…

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Q: dz Given z + 6√√-6x+y=√√√−y=z= −3, calculate - dx Provide your answer below:

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Q: orem of Calculus (a) ²7x²³ + x² − 7x+1dx, - 4 +126x+6 dr (b)

A: Since you have asked multiple question, we will solve the first question for you as per our guide…