Find an equation of the line tangent to the curve at the point corresponding to the given value of t. x=t²-2, y = t³ + 6t; t = 2 7 (Type an equation. Type your answer in slope-intercept form.) ...

Q: If f(x) = 7x² f'(2) = f''(x) = f''(2) = 8e, find:

A: The given function is fx=7x2-8ex

Q: dy dx ey- 1 y ex y(0) = 2

A: Topic:-  application of integration

Q: Let Ln denote the left endpoint sum using n subintervals and let Rn denote the corresponding right…

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Q: A piece of cardboard measuring 12 inches by 8 inches is formed into an open-top box by cutting…

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Q: There is no nonzero vector field F such that V F = 0 and Vx F = 0, simultaneously. O True False

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Q: A license plate must contain 2 numerical digits followed by 2 letters. If the first digit cannot be…

A: Given 1. A license plate must contain 2 numerical digits followed by 2 letters. 2. the first digit…

Q: Express the Cartesian coordinates (-1,-√3) in polar coordinates in at least two different ways.…

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Q: Find the absolute maximum and minimum values of the function over the indicated interval, and…

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Q: Find the exact value of the expressic ܪܕܐ -1 sin sin ၁ 5 သ | O 2n O 2n 5 5 Эт O 3n 5 3 5

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Q: Consider the region in the fourth quadrant between the circles x² + y² = 4 and x² + y² = 25 and…

A: answer is in next step. please give a like !!

Q: Consider the function f(x) = 3 - 3x² on the interval [-3, 6]. Find the average or mean slope of the…

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Q: Find the limit, if it exists. sin(4x) x Ilm

A: To find the following limit, if it exists.limx→∞ sin 4xx

Q: Find the absolute maximum and minimum values of the function over the indicated interval, and…

A: To find the absolute maximum and minimum values of the function over the indicated interval, and to…

Q: them, it exists. 7x² + x 4x² + 6x² + x Ilm

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Q: 9.   The nth term of the series has a factor  xn.  Find the range of x-values for which the ratio…

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Q: dimensions

A: Please refer to the image below

Q: Find the exact sum of the following series (0.25)" (0.25)³ Σ(-1)n-1 n 3 n=3 (0.25)4 4 + (0.25)5 _…..…

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Q: For Questions 1-3, use the differential equation given by y = x, y dy xy dx y > 0. 3. Find the…

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Q: A street light is at the top of a 12 ft. tall pole. A woman 6 ft. tall walks away from the pole with…

A: As per the guidelines  we have to solve only one question at a time. Please repost another…

Q: 1).  Apply the ratio test to the series. ∞ n! 6n3 n=1 Find the limit    lim  n→∞  an+1 an .…

A: Concept: Ratio Test: (1):  If limn→∞an+1an=L<1 , then ∑n=1∞an is convergent (2): If…

Q: 15. Use a suitable change of variables to determine the indefinite integral. [1²cos² (1³) sin(1³)dt

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Q: A spherical snowball is melting in such a way that its radius is decreasing at a rate of 0.2 cm/min.…

A: We have to find the rate of decreasing of volume.

Q: Set up a triple integral using spherical coordinates that finds the volume of the solid bounded…

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Q: Question 1 Nondifferentiable graph.png Find the x-values (there are three values) from the graph,…

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Q: jw F(w). jw F(W) = ·A TAW [9 - acos(wr) -2A (1 - cos (WT)). Tjw jw F(W) = -2A ((asin ² (WT)) 2 Tjw…

A: To explain the encircled step.

Q: Evaluate the interated integral: LS-² x² sin(y) dy dx

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Q: A botanist is studying the development of a bamboo plant. She started keeping a log of its growth 25…

A: Total time= 25 weeks Given that the plant has grown an average of 35 inch each week.  So the plant…

Q: For the cost function C(x) = 2950 +670 +0.8x2 and the demand function p(x) = 2010, find the…

A: Given: Cost Function C(x) = 2950 + 670x + 0.8x2 Demand Function p(x) = 2010 Find the production…

Q: Find the Cartesian equation for the curve represented by the polar equation, r = 2 sin 0. O x² + y²…

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Q: Find the limit. Use l'Hôpital's Rule if appropriate. To enter ∞, type infinity with a lower case i.…

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Q: 12. g = ²+1 - 4 2

A: The given problem is solved below in detail.

Q: Question Find the average value of f(x) = 5 cot (x) csc (x) - 2 over the interval [] Submit an exact…

A: As we know that; The expression for the average value of the function over the interval a,b is:…

Q: The surfaces p = 3 and 5, p = 100° and 130°, and z = 3 and 4.5 identify a closed surface. (a) Find…

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

Q: 3. I Find all eigenvalues and eigenvectors of: [100] 4-6 A = 0 0 2 0 2 0

A: We have to find eigen values and vector

Q: Question 8x + 1 Find the domain and range of f(x) 8x - 8 Express your answer in interval notation…

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Q: Example: find the complex Fourier expansion of the periodic function shown below f(x) = cosx…

A: Basic definite integration is done

Q: Consider the function f(x) Find the value of A: A = - 4x² + 4x 1. f(x) has a critical point at x =…

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Q: π Consider T3 (x), the 3rd degree Taylor polynomial of f(x) = cos(x) centered at a = 4 Use the…

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Q: Gravel is being dumped from a conveyor belt at a rate of 20 cubic feet per minute. It forms a pile…

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Q: Suppose that the DE y"" (x) + 7y(x) =70 2³ +123 has a solution of the form y = Az³ + B Find the…

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Q: ex + ex 11. y=e-ex

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Q: . For what value(s) of x is the tangent to y = 5 (3x-12)4 horizontal? A) -103, 680 B) -4 C) 4 D)…

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Q: LINEAR DE: FIND THE INTEGRAL FACTOR AND THE GENERAL SOLUTION

A: This question can be solved using the concept of linear differential equation.

Q: ["[" f(2,3) dy dr True False [1 f(x, y) de dy

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Q: y= e2x+1 e-1

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Q: Let r(t) = cos(t) i + 4 ln(t² + t)j + 5 tan¯¹(t) k. Find 7' (t).

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Q: What region R in the ry-plane minimizes the value of the following expression? f (x² + y² - 9) dA R…

A: The given double integral ∫∫Rx2+y2-9dA we have to find the region R on the  xy-plane that minimize…

Q: Find the Indefinite Integral. (Remember to use absolute values where appropriate. Use C for the…

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Q: The area of a semicircle of radius 1 can be expressed as S√₁-2²dx Use the substitution x = cost to…

A: This question can be solved using the concept of definite integrals.

Q: (x² - 1)y" + (x + 1)y' - y = 0

A: We have to solve the given differential equation by power series .