Use a graph to estimate the coordinates of the lowest point on the curve x = t³ - 31, y = 1² +1+1. Then use calcu lus to find the exact coordinates.

Q: Find an equation of the plane with the given characteristics. The plane passes through (0, 0, 0),…

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Q: The graph of a function f is shown below. 6 -1 -2 1 Suppose the function g is defined as g(x) Fill…

A: In this question , we can find the limits of the function. Check when 'x' approaches to 'a' , the…

Q: Question 7  A business spends $80,000 on Marketing, $100,000 on R&D,  and $ 12,000 on Expenses.…

A: We have to find the ratio between spending.

Q: Evaluate the following limit using L'Hospital's rule. Enter an exact answer. Provide your answer…

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Q: 3. Find an equation for the parabola with directrix at r = 3 and focus (-1,-1). Find the two latus…

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Q: Use finite approximations to estimate the area under the graph of the function f(x) = x² + 1 between…

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Q: Consider the polar curves C₂: r = 4 cos 0 and C3 : r = 4 sin 0. (a) Set up the integral that gives…

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Q: Let C₁ be the curve with parametric equations I= cost, y = sint -t, where t € [0, 1]. (a) Find the…

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Q: gra Ốf j at point (b) Find the directional derivative of f at the point (0,–2) in the direction of…

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Q: A line has slope and passes through the point (a, b). Which of the following is not a point on l?

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Q: For items 1-5 A 10-ft ladder is leaning against a house on flat ground. The house is to the left of…

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Q: x³Væ² + 1 dx

A: Solve the integration

Q: If f(x)=3+3x−5x^2 find f′ (-3).

A: Solution: f(x)=3+3x−5x2

Q: 6. A parallelogram is defined by the vectors (4, 3) and (1, 2). Determine the perimeter of the…

A: The parallelogram is defined by the vectors (4,3) and (1,2)  We have to determine the perimeter of…

Q: Find the length of the curve r(t) = e³t cos(t), y(t) = et sin(t) for 0 < t < 10. Give an exact…

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Q: The Cartesian equation of the straight line tangent to the plane curve given parametrically by the…

A: Explanation of the answer is as follows

Q: A farmer wants to construct a fence around an area of 6936 square feet in a rectangular field and…

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Q: Find an equation of the tangent line to the graph of the function at the given poin y = x²ex - 2xex…

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Q: Use Part 1 of the Fundamental Theorem of Calculus to find the derivative of the function. g(s) : (t…

A: I am attaching image so that you understand each and every step.

Q: Weather condition Sunny Cloudy Rainy Snowy Percentage of days 42% 31% 18% 9% A) 1240 B) 3300 C) 2100…

A: Number of days in 2008 = 366 ( leap year ) Number of sunny days  =42%*366=0.42*366 Number of people…

Q: Find the Taylor series generated by fat x = a. f(x) = exa=3 Ο Α.Σ Ο Β. Β. €3(x-3) n! €3(x-3) (n+1)!…

A: Find Taylor series.

Q: g(t) How many people contracted the lu 7. Suppose that f(t) is the rate at which snow is falling at…

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Q: Let f(x) = x². a) Find the tangent line to the graph of the function at x = 9. y = b) Find the…

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Q: For the function, find the relative maxima, relative minima, and horizontal points of inflection.…

A: The given function,  y=13x3+x2-8x+15

Q: nd the maximum profit and the number of units that must be produced and sold in order to yield the…

A: Given the query is to find the maximum profit.

Q: A polynomial P is given. P(x)=x^3+64 A) find all zeros of P, real and complex, B)factor completely

A: Explanation of the answer is as follows

Q: x²+x dx (x²+1)(x+2)

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Q: A rectangular swimming pool is 20.0 ft wide and 50.0 ft long. The bottom slopes evenly (lengthwise)…

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Q: 4 2 + Find the area of the portion of the Sphere x² + y² +2²= 9 between the planes Z=1 and 2 = 0.…

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Q: Solve the integral below using integration by part. [(2x - 3) 3) e* dx

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Q: n of Calculus to find the derivative of the

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Q: (x, y) is equal [where we set It is known that the area of a polygon with vertices (x1.₁), (x2.2).…

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Q: Find the indefinite integral. Solution in handwritten. 1. fx sin x² dx

A: Indefinite integral

Q: 4) A degree 3 polynomial function, P(x) has zeros x 2, x = 1, x = m and a leading coefficient of 1.…

A: Here, the polynomial P(x) is of degree 3 and has three zeros x=2,1 &amp; m and the leading…

Q: Let F(x) = f(g(x)), g(2) = -2, g'(2) = 4, f'(2) = 5, and f'(-2) = 7. Find the value of F'(2). Let…

A: 1st we have to differentiate the given function and  then put the given value.

Q: [2 xe3 dư =

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Q: analyze and trace the given curve y = x / (1 - x)2

A: To solve the following problem

Q: Find the area of the region bounded by the graphs of the equations. y = Vx -1, y = 2, y = 0 , x = 0…

A: We have to find the of the  region bounded by the given equations.

Q: Find the orthogonal trajectories of the family of curves x² - y² = (² A x² + y²=C² B) xy=C (C) x-y=C…

A: We can solve as follows

Q: The following is a graph of y = f(x) A= (0,8) You Select the correct graph for the following…

A: We have to find out the graph

Q: A 10-ft ladder is leaning against a house on flat ground. The house is to the left of the ladder.…

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Q: Consider the polar curves Cı :r = 3 sin 20 and C2 : r = 3 cos 0, and let R be the shaded region as…

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Q: 5. y = 2 sin x y

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Q: 304² 3x Evaluate dx dy, by first Reversing the order of integrals. √36 + x3 Enter an integer or a…

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Q: roblem 5. A cup of coffee has temperature of 200 degrees Fahrenheit and is placed in a room that has…

A: Topic:- Newton law of cooling

Q: Given sinα=0.802 and sinβ=0.812 with both angles' terminal rays in Quadrant-I, find the following:…

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Q: Show the repeating decimal .2727272727 repeating.... as an infinite geometric series. Give sum of…

A: This question can be solved using the concept of infinite geometric series.

Q: d Calculate [r₁(t) · r₂(t)] and [r₁(t) × r2(t)] first by differentiating the product directly and…

A: Given    differentiate

Q: Find the line integral of f(x,y) = y ex² along the curve r(t) = 4t i + 3t j, −1≤t≤2. The integral of…

A: Use derivative for finding the line integral.

Q: Find the arc length L of the graph of r(t). r(t) = 1³ i + 1 j + = √61² k, 3≤1≤7

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