The sum of two non-negative numbers X and Y is 15. Determine the values of X and Y that minimize the value of x² + 2x2 X = Number Y = Number

Q: Consider the function f(x) = x¹ - 18x²+2, -2 ≤x≤ The absolute maximum of f(x) (on the given…

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Q: Let F(x) = f(f(x)) and G(x) = (F(x))² . You also know that ƒ(5) = 8, ƒ(8) = 2, ƒ'(8) = 9, ƒ'(5) = 14…

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Q: Consider the equation below. (If an answer does not exist, enter DNE.) f(x) = 3 sin(x) + 3 cos(x),…

A: Consider the function (a) The intervals on which the function is increasing or decreasing can be…

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Q: Let P(h) = 68 exp(-1.5h) where we are using "exp" to denote the exponential function with base e.…

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Q: A company wants to produce an open-top container made of sheet metal with a volume of 10 m³.…

A: Let the length of the box  mLet the width of the box  mLet the height of the box  m

Q: 2. Find all numbers of b such that the average value of f (x) = -9x² + 10x + 4 on the interval [0,…

A: f(x)=-9x2+10x+4Interval [0,b]Average value = 5

Q: Calculate the tangent plane for the function f(x, y, z) = ecos(x)+sin(y+z) at the point (7,0,0).

A: To calculate the tangent plane for the function  at the point .

Q: The value of c that satisfies the Mean Value Theorem on the interval [0, 5] for the function f(x) =…

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Q: x² For the given cost function C(x) = 128√√x + find 42875 the following. For average and marginal…

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Q: Determine the open intervals on which the graph is concave upward or concave downward. (Enter your…

A: to find the open intervals wheref(x) =(x-6)/(8x+7)  is concave upward and concave downward.

Q: Calculate dy dx = dy. You need not expand your answer. dx y = (7x² + x)(x - x²)

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Q: The graph of f is shown in the figure. y 8 7 6 5 4 3 2 1 (a) Evaluate 1 9 [₁ 2 f(x) dx. 3 4 5 6 7 co…

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Q: Theorem 1 Sequence Defined by a Function Let f(x) be a function defined on [c, oo] for some constant…

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Q: find the derivative  f(x)=log|tanx|

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Q: 6) (7.3) Find the Laplace transform L{f(t)} for f(t) = = t, -t +4, Ust 1≤t<2 t≥ 2

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Q: (b) π/2 Jo 1 2 3 4 567 This graph is a rose curve , with equation 0

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Q: 47. lim- v-3 48. lim y-2 49, lim x-2 v-1-√²-5 v 3 y²+y-6 50. lim x 2 50 51. lim x18 8-y²-y x² - 4x +…

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Q: Find the most general antiderivative of the function. (Check your answer by differentiation. Use C…

A: f(x) = 1/5 - 9/x             ,x&gt;0

Q: Which is a rule for a quadratic function represented by a parabola with a vertex at (-1,-3) that…

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Q: Use the formula for the sum of a geometric series to find the sum or state that the series diverges…

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Q: Evaluate the iterated integral. 1-z² 4 [²6² 0 0 28zey dx dz dy √₁-₂² (14e²-14) 2 V1- Z ×

A: In triple integrals if the limit of the integral are not related then we treat all else variables as…

Q: Determine whether the series converges, and if so find its sum. 1 (k+4) (k+5) (Enter DNE if the sum…

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Q: = 3xe 2 on the interval [-3,3]. , and the maximum value is y Find the global maximum value of f(x) =…

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Q: The velocity of an object is shown in the graph below 5+ 4 Velocity (m/s) N لا 3 1 1 pasij 3 Time…

A: The velocity of an object is shown in the graph below.To calculate the total distance traveled over…

Q: Convert the point from cylindrical coordinates to rectangular coordinates. Зл (x, y, z)= 6, × )

A: Given  cylindrical coordinate is .We know in rectangular coordinates,

Q: Use the function f(x) = 15x¹6 — 16x¹5 to answer the following questions (a) Find the interval(s) on…

A: The given function is

Q: 3 The function f(x) = √(x − 1)² does not satisfy the conditions of the Mean Value Theorem on the…

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Q: Differentiate the following function. f(x)=9-4x+5ex f'(x) =

A: Given,

Q: Determine whether the geometric series is convergent or divergent. 36 216 7 + 6 + + 7 49 O…

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Q: Write S = Σ n=5 SN = S = 1 n(n-1) as a telescoping series and find its sum.

A: The given series is the summation of 1 /[n(n-1)], n from 5 to infinity.

Q: f(x)=x^4-4x^3 Does f (x) have any local maxima? If so, where? and what are the local maximum…

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Q: Determine the first three nonzero terms in the taylor approximations for the given initial value…

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Q: A baseball team plays in a stadium that holds 64000 spectators. With the ticket price at $8 the…

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Q: Express the point given in Cartesian coordinates in cylindrical coordinates (r, 0, z). A) (³ ( ¹⁄²),…

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Q: Let lim g(x) x 4 = 8_and_lim h(x) = 8 x 4 Determine the value of the limit 2 lim [g(x) - 3]² x→4…

A: Given that To find:-

Q: Use Newton's method with initial approximation  x1 = 1  to find x2, the second approximation to the…

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Q: Use Theorem 1 to determine the limit of the sequence or type DIV if the sequence diverges. an = TL…

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Q: Find an equation for the conic that satisfies the given conditions. parabola, focus (-10, 0),…

A: Focus : Directrix:  x=2

Q: Given that 1 1-x = M8 n=0 x" with convergence in (-1, 1), find the power series for 1 9-x with…

A: Given that

Q: 8. Evaluate the following limits: 1 (a) lim xx x r (- − arctanr) (b) lim x² xxx

A: Here we will find the limit of the given functions on using l hospital rule

Q: (sinn - 3n 5n - - In +∞ (en²t π)}, еп n=1 Please determine if this sequence is convergent or…

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Q: Complete the table by identifying u and du for the integral. [ f(g(x))g'(x) dx [x³√x² +3 dx u = g(x)…

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Q: 4. Find the limit of the following sequences. You can use any method you choose but make sure to…

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Q: Question 2 Complete the table after finding a simplified form of the difference quotient. For the…

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Q: How long (in years) will it take a $200 investment to be worth $300 if it is continuously compounded…

A: The Formula for compounded continuously where P is the amount after time t  is the initial amount…

Q: For the series compute the partial sums: k! k2

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Q: [Ⓡ 1 x(x + 1) Hint: you can use the partial fractions expansion Evaluate the improper integral dx. 1…

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Q: Consider the implicit equation x²2y² = 7, where y is a function

A: x2−2y2=7ddx(x2−2y2)=ddx(7)Using the power Ruleddxxn=nxn−1