Identify the vertex for: f(x) = x² +5x-2 O (-2,--5-) O (--/ -2) O (--/ -33) 33 O ( - 11/, --5-)

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

Q: Find all the local maxima, local minima, and saddle points of the function. f(x,y)=6ey-3ye* Select…

A: The function is given as , fx,y=6ey-3yex find all local maxima , local minima and saddle points.

Q: Consider the following graph of the second derivative, f" (x), for some function f(x): 161 12 -4 IN…

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Q: If 3x2 + yx = 9, what is -? dx dx dx = = = 11 -6x-y² 2.xy -6x+y² 2x -6x-y2 2x² 6x-y2 2y 59

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Q: lim x-1 d x3+5 xa - X-5 * ха x2 + 4x -5

A: According to question,Given limit,limx→1 x3+5x2-x-5x2+4x-5

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Q: Find the average height of the paraboloid z = x² + y² over the square 0≤x≤3, 0≤ y ≤3. The average…

A: Given data The equation of paraboloid is, z=x2+y2. The limits of the square is 0≤x≤3, 0≤y≤3.

Q: Evaluate Solution √²+z²dv, where E is the region bounded by the paraboloid y = x² + z² and the plane…

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Q: Find the linearization L(x) of f (x) = In(1 + x) at a = 0. Use this linearization approximate…

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Q: Problem 3 d²y(t) — 4 dy(t) + 4y(t) = 2 × e²t dt² With initial conditions y(1) = 3, dy (1) dt = 1

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Q: (a) Find an equation z = x² - y², of the tangent plane to the surface at the given point. (3, 2, 5)

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Q: d dx [ 3+√√f(sin( sin(x)) cos(x) f' (sin(x)) 2√f(sin(x))

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Q: Direction: Analyze the given problem. Show your complete and detailed solution (Given, Unknown,…

A: Solution: Given data, Let the width and length be x and y respectively. area = 2000 Sq.ft.…

Q: 19. f(x) = sin²: x cos 2x, 0<x<T

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Q: 3 Integrate f(x, y) = y(x² + y²)³ over the domain x² + y² ≤ 25, with y ≥ 0. Added 55 Pak Young FGS…

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Q: Question: is there a logarithmic property thay says: ln ∣ a - b ∣ is equal to - ln ∣ a + b ∣   Im…

A: Two concepts Trigonometry equations Logrithmic rule

Q: 3. Determine whether Rolle's Theorem can be applied to Ax) = -x² + 10x on the closed interval…

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Q: Match each of the trigonometric expressions below with the equivalent non-trigonometric function…

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Q: Evaluate the integral Note: Use an upper-case "C" for the constant of integration. -2 12²=2² da

A: To evaluate the following integral. ∫-2x4x2-2 dx

Q: Determine whether the series is convergent or divergent by expressing the nth partial sum s as a…

A: We can prove the convergence by using nth partial sum of the given series.

Q: Calculate the double integral. Sk [[[x sec²(y) dA, R = {(x, /1105x58,0sys X y) y) | ≤ ≤ ≤ R 2}

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Q: find the equation of the line 9. Through (2, –50) with equal intercepts 10. Through (–7, –4) with…

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Q: In 2012, U.S. consumption of renewable energy was 8.45 quadrillion Btu. Since the 1960s, consumption…

A: Solution: Given: f′(t) = 0.004t + 0.062 To find f(t), we need to integrate the given rate of growth…

Q: 78. 1 2 4x + 12 2 (x² + 6x + 1) dx

A: Ans = 9/68 For detail ...go through the solution I have solved step by step in detail

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Q: 15. Evaluate the limit for the graph: lim f(x). *→2* 4 +∞o a. b. -1 14 A 2 -2 0 2 A C. d. 2 does not…

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Q: Is this fully simplifed ?

A: Find y' for the function y=6x-3x2+7x.

Q: (2). z=x² + y,k=-4,-1,0,1,4.

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Q: Write the exponential equation for the function going through the points (4,8) and (2,-6) and has a…

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Q: What is the relative minimum value of the function f(x) = 5-6x - x²? Of(x) has a relative maximum…

A: Since you have asked multiple questions, As per the guidelines we have to solve the first question.…

Q: Find the distance from the point (-5,1,2) to the line a(t) = (-5,0, 3)t + (-7, 1, 5) -

A: According to question,Given Point : -5,1,2,Given Line : a⇀t = -5,0,-3t+-7,1,-5

Q: 5+5x2 lim x→∞ (3+7x)

A: Here is the solution:

Q: Evaluate the following limit. lim 1+ X→∞ lim X→∞0 1 2 3 X 2 3 X In x Inx = (Type an exact answer.)

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Q: Suppose that f is a differentiable function such that ƒ(3)= 4 and ƒ′ (3)= 3. Compute d 2 da [x² +…

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Q: Fully factor and find all of the specific zeros of the function f(x)=2x4-9x³ + 6x² - 9x +4 Show your…

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Q: Consider the four graphs shown below. For each graph, select Yes if satisfies the following…

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Q: Let r(t) = (t², 1 — t, 4t). Calculate the derivative of r(t) · a(t) at t = 2, assuming that a(2) =…

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Q: Find the equation of the curve for the given slope and point through which it passes. Use a graphing…

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Q: 2.) Find the volume of the solid whose base is bounded by the circle whose center is the origin,…

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Q: Use the gradient to find the directional derivative of the function at P in the direction of PQ.…

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Q: 5. Find the points of inflection and discuss the concavity of the function (x)=-8x-2 cos x on the…

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Q: Find an equation of the tangent line to the curve at the given point. y = 9ex cos(x), (0,9) y =

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Q: Use the method of cylindrical shells to find the volume of the solid obtained by rotating the region…

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Q: Calculate the double integral of f(x, y) = over the triangle with vertices A=(3,7), B = (8, 12), C =…

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