Find the critical numbers of the function. (Enter your answers as a comma-separated list.) g(x) = x² - 7x5 7x6 4 -35x x = 7x X

Q: Find the indicated nth partial sum of the arithmetic sequence. a₁ = 13, 316, n = 120 120 =

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Q: [ 8®in}x sin 3 xdx (Ans: 3/8 sin²x In 8 + C) Hint: Use 2 sin cos 0 = sin 20

A: To evaluate the integral

Q: Find the limit (if it exists). (If an answer does not exist, enter DNE.) lim_(ti + sin(t)j +…

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Q: Verify the identity. (Simplify at each step.) 5/2 sin 1/2 1/2 sin X COS X - X COS X - sin 5/2 sin X…

A: Here we have to verify the identity.

Q: 3 (1 + 2x - 4x³) dx

A: The given integral is ∫131+2x-4x3dx

Q: Use a definite integral to find the area under the curve between the given x-values. f(x) = ex from…

A: Topic- Area using definite integral

Q: Find the following for the given equation. r(t) = (e¯t, 3t², 6 tan(t)) (a) r'(t) = (b) r"(t) = (C)…

A: Given:         rt=e-t,3t2,6tant a)   r't=ddte-t,ddt3t2,ddt6tant              r't=-e-t,32t,6sec2t…

Q: Q5. (Log,3)= a); xin & Cost (1 ²)dt

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Q: Determine which of the following statements are true and which are false. Enter the T or F in front…

A: As per the guideline, we can solve one question at a time in case of multiple questions. As you have…

Q: Use the definition of the Laplace transform to find L{f(t)}. (Enter your answer in terms of s.) f(t)…

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Q: Find the inverse Laplace transform of the given function. 7! (s — 5)8 NOTE: Express your answer in…

A: The give Laplace transform is Fs=7!s-58

Q: B- Find the local extreme points of the function f(x, y) = 4xy - x - y^.

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Q: object from v? If yes, explain how would you recover s. If not, what other information are we…

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Q: a.      A scaled version of shape A was needed, such that its new coordinates become (-2,8) (8,6)…

A: Given data: new coordinates become (-2,8), (8,6), (10,-4), (0,-2)

Q: Find the center of mass of the given system of point masses. (x, y) = = mi (X,Y) (2, 1) 4 2 (-3, 2)…

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Q: Find the domain of the vector-valued function. (Enter your answer using interval notation.) r(t) =…

A: The Domain of the function is the set of all possible input values for which function is defined.

Q: Consider the graph of the function g given by g(x) = n(x2+1) for 0 0. 0.81 0.6 0.4 0.2 0 20 40 60…

A: Given data:- The given function, g(x)=ln(x2+1)x         for (0<x)

Q: Evaluate (2x² - 4x + 1)² dx. √

A: Given data:- ∫x32x3-4x+12dx

Q: The height h (in feet) above ground of a seat on a Ferris wheel at time t (in seconds) is modeled by…

A: Solution h(t) =A sin(Bt - C) + D Given: h(t) = 51 + 49sinπ13t-π2

Q: Describe the graph of the equation: r = 6ti − 9j + (1 + 8t)k. [Choose the correct answer.] O The…

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Q: H.w: Find the LT of the following functions: 3-f(t) = cosh at cos at

A: Given, f(t)=cosh at cos at

Q: (Question #1, 2, 3, 4, f(x)=x²e* f(x) = et'nx f(x) = ln(4x³ + x) 1. 2. 3. ror the following…

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Q: Use Definition 7.1.1. DEFINITION 7.1.1 Laplace Transform Let f be a function defined for t > 0. Then…

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Q: Find r(t). u(t). r(t) = (3t − 4)i + ¹1t³j + 4k 4 u(t)= t²i - 8j + t³k r(t). u(t)= Is the result a…

A: To find: rt·ut Given information: rt=3t-4i+14t3j+4k ut=t2i-8j+t3k

Q: Find the Laplace transform of the function: O O O : ²2² (2²/1 + ² ) L(s) = e²s 2 0-²₁ (²/17 - 1²/7)…

A: To find the Laplace transform of the function: ft=0,      t<2t2-4t+6,     t≥2

Q: Solve the equation on the interval 0 ≤0<2 cos (30)=1 MAN What are the solutions to cos (30) = 1 in…

A: Solve the trigonometry equation

Q: Find the solution to the differential equation dy/dx + y^2sin(x) = 0 which satisfies y(0) = −1.

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Q: Question A particle moves along a line with a velocity v(t) = t2-9, measured in meters per second.…

A: Here, the velocity of the particle is: v(t)=t2-9 Now, v(t)=0⇒t2-9=0⇒t2=9⇒t=-3,3

Q: Q10) f a)x² + c sin"1x+cos-ix dx +c c)= x + c 12 +

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Q: Determine whether f is continuous, piecewise continuous, or neither on the interval 0 ≤ t ≤ 3. 31²,…

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Q: Find the equation of the sphere of radius 8 centered at (1, 3, 6). O x² + y² +z² = 46 O x² + y² + z²…

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Q: Consider the function f(x) = 5x + 7x7 - 3x¹ - 5. An antiderivative of f(x) is F(x) A is and n is and…

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Q: Assume that x and y are both differentiable functions of t and find the required values of dy/dt and…

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Q: Evaluate if possible 1 [₁²x5+¹ dx -2 x3 ….…..

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Q: 4. Verify that the y defined below satisfies the following boundary value problem. -x Sy" = 8(x -…

A: The Dirac delta function is defined such that ddxHx=δx, where Hx=1x&gt;00x≤0is unit step function.…

Q: Use appropriate algebra and Theorem 7.2.1 to find the given inverse Laplace transform.(Write your…

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Q: Find: S x² √√x – 3 dx =? A. (x-3) - (x − 3) ²/7 = 2 − 3)² + 6(x − 3)² + c B. ² (x − 3) − § (x − 3) %…

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Q: A tank contains 300 liters of fluid in which 10 grams of salt is dissolved. Brine containing 1 gram…

A: Given problem:- A tank contains 300 liters of fluid in which 10 grams of salt is dissolved. Brine…

Q: Find the limit. Use l'Hospital's Rule where appropriate. If there is a more elementary method,…

A: To find the given limit using l'Hospital's rule. limx→0+sin(x) ln (9x) Here, the function is of the…

Q: A large tank is filled to capacity with 700 gallons of pure water. Brine containing 3 pounds of salt…

A: We are asked to find the  number A(t)  of pounds of salt in the tank at a time t

Q: D O 413 O 02 00 Question 5 04 Evaluate the limit limo tan(+h)-tan() h by recognizing it as a…

A: limh→0tanπ3+h-tanπ3h   The definition of the derivative of a function f(x) at x=a is given by:…

Q: f(x) is continuous on (-∞,∞). Use the given information to sketch the graph of f. f'(0) = 0, f'(-11)…

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Q: Estimate the area between the x-axis and the graph of f(x) = 9 - x² over the interval [0, 3] by…

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Q: Evaluate the integral arc y = x² from (0,0) to (1,1). NOTE: Enter the exact answer. (2x + 18y)dx +…

A: Given integral is ∫C(2x+18y)dx +(3x-y)dy We have to evaluate given integral along a parabolic arc…

Q: The region bounded by f(x) = - 2x² + 8x + 24, x = = 0, and y = the volume of the solid of…

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Q: Suppose that f(x,y,z)=(x,y,z)=2x+4y+3z at which x^2+y^2+z^2≤3^2 Absolute minimum of…

A: Please see the below picture for detailed solution.

Q: The surfaces r = 2 and 4,0 = 30° and 50°, and p = 20° and 60° identify a closed surface. (a) Find…

A: Disclaimer: since you have posted multiple sub part of a question,we will solve only first three for…

Q: lim, 0 6 tan² (5x) 15x²

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Q: Question 4 Which among the choices is not true about the continuity of f(x)? if x 1 -{₂ f(x) = x²,…

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

Q: Find a degree 3 polynomial that has zeros -3, 2 and 5 and in which the coefficient of ² is - 12. The…

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