The system of differential equations : has the solution Y = C₁ et V₁ + C₂ ezt V₂ + C3 e¹³ V3 where (in increasing order A₁ < A₂

Q: Let + f² f(x) dx = 3, Find S 4 f(x) dx = -10 5 ¹ [*³ f(x) – 6 and - 3 dx = f(x) dx = 3, [ f(a) f(x)…

A: The Sum Rule:The Power Rule:The Constant Coefficient Rule:

Q: dx f(x) g(x)]-

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Q: at the point (0, 1/2). and b = The equation of this tangent line can be written in the form y = mx +…

A: y=1/[3sinx+2cosx]Point (0,1/2)

Q: Simplify the following rational expression. State the domain restrictions: a) x3-8 2x3-8a

A: To simplify the following rational expression and to state the domainrestrictions.

Q: Find the volume of the region under the surface z=xy^2 and above the area bounded by x=y^2 and x+y=2

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Q: 1) Write a complex number in a standard form z = x + ly:: 2+i (2- i)(3i+ 4)(i+1)

A: The given complex number is

Q: Find the integral of the following function by parts So 0 sec²0 de Ja where a = 6.08, b = 7.05 in…

A: The given integral is

Q: What substitution(s) would make the following integral simpler? I.e., simple enough to integrate by…

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Q: logarithms. Express powers as factors. 1. A 50-mg sample of a radioactive substance decays to 34 mg…

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Q: 61. Presale Order A wireless store owner takes presale orders for a new smartphone and tablet. He…

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Q: Using the Rules for Finding the Derivative of a Function. For the following exercise, assume that…

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Q: The table shows the total assets (in trillions) held in a foreign bank for the given years. Complete…

A: We have to find the function using table values

Q: Find the indicated term of the binomial expansion. 13 (u³ +21²) ¹³₂ ; tenth term

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Q: Find the demand function for the marginal revenue function. Recall that if no items are sold, the…

A: R'(x)= 0.03x2-0.08x+189

Q: Find parametric equations that describe the circular path of the following person. Assume (x,y)…

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Q: Suppose that AABC is a right triangle with ZC = 90°.

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Q: Use logarithmic differentiation to find y = secx tex Secx dy dx 4 for: x² +1 e 8x secx

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Q: = (a) The fourth Taylor polynomial for f(x) = ln (sec(x)) at a co + c₁x + ₂x² + 3x³ + ₁x² where Co =…

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Q: y = In[sin(x + y)]

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Q: please i dont understand that you did after step 3 from 0=sin(2pi c)

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Q: 3/4 Find the cost function if the marginal cost function is given by C'(x) = x C(x) = +5 and 16…

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Q: Evaluate the following definite integral. π JU OA. (( sin 8t)i + (cos 8t)j + (10t)k) dt Select the…

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Q: Use the Alternating Series Remainder Theorem to determine the smallest number of terms required to…

A: The objective of this question is to find the smallest number of terms required to approximate the…

Q: Compute the indefinite integral of the following function. r(t) = te'i +t² cos t³j 3 4t 4 k Select…

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Q: Find the absolute minimum and absolute maximum of f(x, y) = 192x³ + y²(1 - 4x) on the triangle with…

A: Given function is Now, we have to find the absolute minimum and absolute maximum for the above…

Q: Assume that y is the solution of the initial-value problem 5 sin x If y is written as a power series…

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Q: 19. Use Newton's Method to estimate the one real root of f(x)=x²+2x-2. Start with x = 1, and perform…

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Q: For what value of x the geometric series (x-4)" 9n is convergent?

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Q: Evaluate the given definite integral. HAL 5 - dy Y

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Q: =e*² and y = x²e² don't have elementary antiderivatives, but y = (2x² + 1)² does. Evaluate [ (2x² +…

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Q: Find the equations of the tangent and normal lines to the graph of the function at the given point.…

A: The equation of the tangent line  to the curve y= f(x) at x= a is  The equation of the normal line…

Q: 15. A hot-air balloon is rising straight up at 5 ft/sec. An observation area is located 80 feet from…

A: Hsnsnsn

Q: SX7UPET dx

A: I=∫x7x4+1dxI=∫x4(x4+1)x3dxI=14∫x4(x4+1)4x3dxSubstitute x4+1=u

Q: For what value of a is the following function continuous at every x? f(x) = x²-30, x<10 x≥ 10 ax,…

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Q: 1. For the function g(x) graphed here, find the following limits or explain why they do not exist.…

A: Since the subparts a,b and c of question 1 have been answered i suppose you want the answer for part…

Q: Give equation

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Q: D. Find the following limits. You may use any theorem we have proved, such as Arithmetic of Limits.…

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Q: Given that f (t) = t² - t - 5 represents the rate at which air is escaping from a balloon in liters…

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Q: Use the parametric equations of an ellipse, x = a cos(8), y = b sin(0), 0 ≤ 0 ≤ 2π, to find the area…

A: Given that the parametric equation

Q: f 9 csc (2) sec (2) dx Evaluate the integral above by taking the derivative of each answer choice to…

A: We have integrate the given expression

Q: 57. Orbital Launches In 2012 there was a total of 78 commercial and noncommercial orbital launches…

A: In 2012 there was a total of 78 commerecial and noncommerecial orbital launches worldwide. In…

Q: Let g(t) = - 503 t Determine the most general indefinite integral of g. - 5 + dt

A: Given,

Q: Determine whether the geometric series is convergent or divergent. If it is convergent, find its…

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Q: Evaluate this integral | √2 3 (1+x) + C √x(1 + x² ) 5 dx (1+x)³ +C 3 ○ 2 √ (1 + x ³ ) 6 + C Va 3 6 3…

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Q: The approximate rate of change in the number of design patent applications received in recent years…

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Q: The polynomial p(x) = 8x³ - 18x² + 7x +3 has exactly 3 zeros. If p(1)= = 0, use synthetic division…

A: Given that the polynomial

Q: Find an equation of the curve whose tangent line has a slope of f'(x)=x given that the point 1,-…

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Q: When a bactericide is added to a nutrient broth in which bacteria are growing, the bacterium…

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Q: 1. Find the equation of the line that goes through the point (1, 5) and is parallel to the line y =…

A: Question No. 1:To find the equation of the line that goes through the point and parallel to the…

Q: The equation z = x² + y² - 2x is given in Cartesian coordinates. Convert the equation to cylindrical…

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