Use l'Hôpital's rule to find the following limit. 1 1 X-7 In (x-6) lim X→7* lim X→ 1 1 X-7 In (x-6) = (Type an integer or a simplified fraction.)

Q: A dinghy is pulled toward a dock by a rope from the bow through a ring on the dock 10 ft above the…

A: NOTE: Refresh your page if you can't see any equations. . here we have y=10 ft (height of the ring…

Q: = .. Find the tangent plane and normal line to the surface ƒ (x, y) : (1, 0, 1). xey at the point

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Q: Solve the equation. Write the numbers using integers or simplified fractions. tan (-3x)=1 Part: 0 /…

A: NOTE: Refresh your page if you can't see any equations. .

Q: Evaluate: Σ 1 (k − 2)(k-1)

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

Q: 1. For 1. For all n > 2, ¹n(n) >2, and the series Σ converges, so by the Comparison Test, the series…

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Q: 4. For all n > 2,3 1, nln(n) < 1/12, and the series 2Σ n' verges. converges, so by the Comparison…

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Q: Consider the graph of f'(x) below. At what value (or values) of x does f(x) have a local minimum? -6…

A: The solution is given below

Q: 4. Find the general solution: y" + 2y(y')³ = 0

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Q: Let f(x) = e* and g(x) = Inx. Then O(A) x ER such that f(g(x)) = g(f(x)) O(B) Vx ER, f(g(x)) =…

A: The answer is given below:

Q: Plot the point whose polar coordinates are given. Then find two other pairs of polar coordinates of…

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Q: Find the points on the lemniscate where the tangent is horizontal. 8(x² + y²)² = 25(x² - y²) y 0.6…

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Q: Evaluate a) 12 b) 08 c) 04 d) O-4 e) -2 [(2²+ + 2x + 1) dx + (2xy + 4y - 1) dy along the given path…

A: We will use parametric equations to solve .

Q: Evaluate each expression using the given table of values:

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Q: Evaluate yda + rydy along the given path C from (0, 0) to (5, 1). C is the parabolic path a = 5y².…

A: Given :∫cydx+xydy over 0, 0 to 5, 1Parabolic path x=5y2

Q: Determine the radius and interval of convergence of the following power series. x2k+1 13k-1 Σ

A: NOTE: Refresh your page if you can't see any equations. .

Q: graph of g(x). 6 Ay 4 3 2 1 −4 −3 −2 −11 2 y=g(x) 1 2 3 4 5

A: If g(x) is the first derivative of f(x), then f(x) has a relative minimum at x=3.

Q: Two cars, A and B, start side by side and accelerate from rest. The figure shows the graphs of their…

A: In order to find the time at which the cars are again side by side, obtain the total numbers of…

Q: Problem #1: Let Problem #1: F(x, y, z)= (6x5 ln(7y² + 5) + 8-4) i + Evaluate 141x6 7² +5 and let…

A: Given Vector function is conservative. We use Total derivative concepts to solve this problem.

Q: Suppose that P dollars are invested at a nominal interest rate of r compounded continuously. Find an…

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Q: Obtain the equation of f(t) or y(t) taking into account the following differential equations:…

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Q: Which of the following is equivalent to A In 5 1.1.5 In 3 udu 5 to fº 5 xlnrer ?

A: NOTE: Refresh your page if you can't see any equations. . use the integration-by-parts method so…

Q: Find the limit of the following sequence or determine that the sequence diverges. 2n {(1+:)³"} {(₁+…

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Q: Find all values of t in the interval [0, 2π] that satisfy the given equation. (Enter your answers as…

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Q: Hi,  Need to work out for Case 2  how did you get (2x2 + 9x + 4 ) + (5x + 6)

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Q: Let f(x) = ex²-1. The set f-¹([1, 3)) is: 75.5. O (A) (-√1+log 3, -1] U [1, V1 + log 3) O (B)[-√1+…

A: NOTE: Refresh your page if you can't see any equations. . the given function is  we need to find…

Q: Marginal Profit  A division of Ditton Industries manufactures a deluxe toaster oven. The daily…

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Q: ƒ'(x) =

A: Topic:- application of derivatives

Q: Suppose tan X=V²₁ cos x = -2V/² 2 J 5 Options A)-VE b)-3 c) SUG Part 1. Find Sin x part 2. Find CSC…

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Q: Use series to evaluate lim X→0 ex-(1+x) 4x²

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Q: Consider the following equation. 3x4 − 8x3 + 2 = 0,    [2, 3] (a) Explain how we know that the…

A: Let's find root of given function.

Q: 5. Find the linear f(x) = √1 approximation of the function x at a = 0 and use it to approximate the…

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Q: At the beginning of a laboratory experiment five baby rats measured 5.3, 6.5, 6.8, 7.2, and 5.9 cm…

A: Solution-   Given  2×5 matrix is      A=  [5.36.56.87.25.9144138153157147]      B…

Q: Use the chain rule to find the derivative of 15 f(x) = 2(3x7 + 7x¹0) ¹5 You do not need to expand…

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Q: solve each inequality.   x2-9&lt;0

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Q: 1. Evaluate the given line integrals where C is the given curve a) y³ds C: x= t³, y = t, 0 ≤ t ≤ 2…

A: Evaluate the given integrals

Q: (5) (6) (7) მე-2 d'y dx² Ərət Ət² √5 + sin x sin 0 = (2-y)dx + (2x − 3y)dy = 0 - d³y d03 cos dy do =…

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Q: 19. Find the distance from the point (3, -2,7) to the plane 4x – 6y + z = 5. Show all necessary work…

A: A detailed solution is given below.

Q: Evaluate the line integral by applying Green's theorem. f(3x² + y) dx + (y²³ + 5 x) dy C: 9x² + 25…

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Q: Cell 130 bo at a price ncrease in per week maximum r

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Q: A street light is at the top of a 15 ft tall pole. A woman 6 ft tall walks away from the pole with a…

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Q: Test.

A: We have to consider the given statements are correct or incorrect according to the given information

Q: An inverted pyramid is being filled with water at a constant rate of 50 cubic centimeters per…

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Q: 10 Consider the function f(x) = 5x¹⁰ + 10x5 – 10x² – 9. Enter the general antiderivative of f(x)

A: The given function fx=5x10+10x5-10x2-9. We have to find the antiderivative of fx.

Q: If 2400 square centimeters of material is available to make a box with a square base and an open…

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Q: Evaluate the geometric series or state that it diverges. M8 n=0 e FIN n 2

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Q: 3. Evaluate ſ¹₂3x² – 2x + 1dx . 4. Evaluate fox√2x² + 1dx .

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Q: Solve the equation 3 ln x = 2. Round your answer to two decimal places. If the equation does not…

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Q: 2 (1) Σπίτ n n=1

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Q: dx

A: See the details solution in below

Q: 2) factor 5²-73 +12

A: Since the student has posted multiple questions and does not mention any specific question, and…