1) Find the equation of the tangent line and normal line to the graph of the function y=x√√x-1 at (5,10).

Q: Use the Laplace transform to solve the given initial-value problem. y'' + 2y' + y = 0,  y(0) = 1,…

A: A detailed solution is given below.

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Q: S 3x+1 - dx x²-x-6

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Q: Evaluate the limit, if it exists. (If an answer does not exist, enter DNE.) x² - 6x + 4 lim X→ 2 X-2

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Q: integrate using partial decomposition (y^2)/(y+1)(y-1)

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Q: ƒ(5x² + 4x³ − 2x + 1)dx 이름 +2 -를 +a + C 5 2 O x5 x5 + x²-x²+x+C O 20x5 + A O 20x³ + 12x² −2+ C…

A: Given, ∫(5x4+4x3-2x+1)dx

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A: Topic:- application of integration

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A: sum of two numbers is 'a', the product of one to the square of the other is to be maximum

Q: g(x)=x-bx³ +a+c. Use calculus to: St (a) Find the critical points of g(x). (Round the y-value to 3…

A: We have to solve given Questions.

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A: We have to find derivative of given function.

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Q: 7- (a) If a is a constant and cannot be equal to 0, find the critical points of f(x) = 3a + 6x (b)…

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Q: A street light is at the top of a 13 ft tall pole. A woman 5.75 ft tall walks toward the pole with a…

A: Given problem:- street light is at the top of a 13 ft tall pole. A woman 5.75 ft tall walks toward…

Q: Find all solutions to 2 sin(0) 0 = = - 1 on the interval 0 ≤ 0 < 2π

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Q: Suppose f(-1) = 1, f'(-1) = 5, and g(x) = x³ f(x). The tangent line to g(x) at x = 1 is given by y =

A: The objective is to find the equation of tangent line .

Q: 21

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Q: differentiate the funtion y = cosh x - sinh x / cosh x + sinh x

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Q: Find the constant a such that the function is continuous on the entire real line. f(x) = √5x², x ≥ 1…

A: We need to find a.

Q: Evaluate the limit, if it exists. (If an answer does not exist, enter DNE.) t²3t- 28 lim t→7 t-7

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Q: 2 1. f(x) = x² + 8x + 12 2 2. f(x) = x² + 25x 150 3. f(x) = x² + 18x130

A: “Since you have posted a question with multiple sub-parts, we will solve first three subparts for…

Q: r H+ sin x sin 2x dx 2 cos X

A: Solving the problem by finding the value of the integration.

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Q: Prove that if i and k are relatively prime positive integers, for every positive integer l the…

A: Concept: Number theory: Number theory is an area of mathematics that aids in the study of the set of…

Q: Determine whether or not the following limits exist (explain why or why not): x² - y² a) lim…

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Q: A graphing calculator is recommended. (a) Find the vertical asymptotes of the function y = X = (b)…

A: Explanation of the answer is as follows

Q: c) What is the loss the company incurs when it tries to maximize sales (that is, produce the maximum…

A: Find out the loss the company when it tries to maximize the sales.

Q: 2. Consider the function F, that assigns x in its domain to x² - 1 F(x) = |x-1| In its domain. a.…

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Q: Given: y = x - sin(2x) Find: dy dx 0 - cos²x 2 ○ - sin² x 01+ cos²x O sin²2 X

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Q: lim h→0 f(1+h)-f(1) B)-f(1) h 5/14 Correct where f(x) = 9x² + x - 4

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Q: Find f'(x): f(x) = sin(2x) O 4sin (2a) (2 ln 4) cos(2x) O 4sin (2x) (2 cos(2x)) O 4sin (2x) (In 2)…

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Q: F(x) = Se* - e*-1 at x = 1 Determine the equation of a line tangent to the curve at x =1

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Q: Solve 2 cos² (x) - 3 cos(x) + 1 = 0 for all solutions 0 ≤ x < 2π X = Give your answers as a list…

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Q: Given f(x,y)= x³(x²y³-2y²), find all of the first and second partial derivatives.

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Q: f(x) = 4x5 (12x² + 15x + 3)

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Q: Find the regions where sinx sx.1

A: Topic:- trigonometry

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Q: For the function f whose graph is shown, state the following. (If the limit is infinite, enter '' or…

A: As per Bartleby answering guidelines if a questions has multiple sub parts then an expert is…

Q: Question 4. A lamina with the density p(x, y) = x² is bounded by the curves y = 3x² and y=x² +2. 1)…

A: Let's find mass of lamina.

Q: Find the area of the region enclosed by the curves y=2 sin x y = 2 sin x and y=2 sin 2x for 0≤x≤ T.…

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Q: 1 Suppose that I is a location function of an object, given as L(t) = We will compute the 3t - 7…

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Q: Let V be the volume of the solid obtained by rotating the region above the x-axis and below the…

A: Recall:  V=∫abπf(x)2dx We have a=0, b=6, f(x)=e-x

Q: An engineering firm recently estimated its total revenue function as TR = 300q - 6q2² and its total…

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Q: 2a Please help me with my reviewer, provide the whole solution so that I can understand thank you

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Q: On your own, verify that the indicated expression is an implicit solution of the given first-order…

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Q: The 33-N force P is applied perpendicular to the portion BC of the bent bar. Determine the moment of…

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Q: Find the volume of the solid obtained by rotating the region bounded by the given curves about the…

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