Express the integrand as a sum of partial fractions and evaluate the integral. 2 48x S (x-9)(x+3)² dx Express the integrand as a sum of partial fractions. S- 48x² (x-9)(x+3)² dx = JOdx

Q: 41. lim [2ln(x-3) - In(3x² + 5)] X-80

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Q: Suppose that f(x, y) = r²- xy + y² - 2x + 2y with D= {(x, y) | 0≤x≤2,0 ≤ y ≤ 2}. 1. The critical…

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Q: Write an equation for a rational function with: Vertical asymptotes at x = -2 and x = -4 x…

A: Here vertical asymptotes at x = -2 and x = -4 we have denominator (x+2) and (x+4) as co-factor .…

Q: 3. The limits below do not exist. Verify this by showing two different pathways that result in…

A: as per company guidelines we solve only first question when multiple question being posted.

Q: Find the general solution in the form y = yc + yp. y'' + 4y' + 5y = e-2tcost

A: y'' + 4y' + 5y = e-2tcost Find genral solution

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Q: 6(x − 1)²

A: We need to find the derivatives of the following expression   Where, fx=6x-17   Useful formula÷…

Q: y" + y = 2, y(0) = 4, y' (0) = 3 (A) y = 2 sint + 3 cos

A: given y'' + y = 2 D2y + y = 2(D2 + 1 ) = 2 for complementary solution D2 + 1 =0D = ±iD = 0…

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

Q: Consider the rational function -4x-4 x² 6x - 7 g(x)= Factor the numerator to get Factor the…

A: Given gx=-4x-4x2-6x-7

Q: 4. A fence is to be built to enclose a rectangular area of 800 square feet. Then fence along three…

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Q: Find an nth degree polynomial function with real coefficients satisifying the given conditions n=3…

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Q: Find the derivative and simplify where possible for the following:

A: Given, g(x)=1-coshx1+coshx   Aim: Find g'(x)

Q: Calculate the derivative: (6t4 - 7t) dt =

A: To find the Derivative.

Q: an+1 Use to show that the sequence given by an (a) (c) Strictly increasing (b) Strictly decreasing…

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Q: 4. Let f(x)=2x4-5x² + 2x sin(x) *20 x < 0 (a) Prove f(x) is continuous everywhere. (b) Prove there…

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Q: 2) What is the difference between f'(x) and f'(7) and how do you say out loud the expression f'(x)?…

A: Difference between f'(x) and f'(7)

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A: The differential equation is given by f''x = x-32                                   ...........1 The…

Q: Sketch in the xy - plane the domain of each function : (a) ƒ (x, y) = (√x + √y) · In (x² + y² − 4) -…

A: Note : Multiple questions : According to our company guidelines we are supposed to solve only…

Q: x² + 1 x³ + 2 has Select an answer ✪

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Q: Use linear approximation to approximation (sqrt√36.1) as follows. Let ?(?)=(sqrt√x). The equation…

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Q: A rectangular metal tank with an open top is to hold 4 cubic feet of liquid. What are the dimensions…

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Q: X Find the area of the region in the first quadrant bounded on the left by the y-axis, below by the…

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Q: Evaluate the integral. (Use C for the constant of integration.) √(x² + 8x) cos(x) dx (x²sin(x) + 8x…

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

Q: I If f(x) = = √² (1²³ + 3t² (₁ (t³ + 3t² + 5) dt then

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Q: then a = NO and b = --2- -1- Check Answer 6 - -1- -2- --3- W --4- LO CO -5 If this function has the…

A: This function has hole at x = -2 And vertical asymptote at x = 3 so Q(x) = (x+2)/{(x+3)(x+2)} so a =…

Q: The total sales of a company (in millions of dollars) t months from now are given by S(t)= 0.041³…

A: Given S(t)=0.04t3+0.8t2+4t+3We need to find(A)S'(t)(B)S(7) and S'(7)(C)Interpret S(13)=278.08 and…

Q: An equation is given. (Enter your answers as a comma-separated list. Let k be any integer. Round…

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Q: An unknown radioactive element decays into non-radioactive substances. In 480 days the radioactivity…

A: The decay formula: Nt=N0e-λtwhere Nt=Amount of substance left after 't' days            N0=Intial…

Q: Graph the trigonometric function. sec Start by drawing three consecutive asymptotes. Then plot two…

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Q: 3. Given h(x) = 3 ln(1 + x²) + 8 arctan(x), find all x where h"(x) = 0.

A: Topic - inflection point of a function We are given h(x)=3ln(1+x2)+8arctan(x)we know…

Q: Find direction Vector a that has the same as (-6,5,67 but has length 4

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Q: = The doubling period of a bacterial population is 15 minutes. At time t population was 90000. What…

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Q: Find the critical points of the function f(x,y) = x² + y² − 4xy + 2.

A: Given, f(x,y)=x4+y4-4xy+2

Q: Describe the triangular region whose vertices are at (0, 0), (1, 0), (1, 2) as set in the polar…

A: Answer is in step 2.

Q: ************** An airplane flying at an altitude of 5 kilometers passes directly over a radar…

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Q: Exercise 6 Limits The following graph of the function f satisfies lim f(x) = 2 . For & = 1.5 find a…

A: Given that limx→3f(x)=2  and ε=1.5

Q: 9. Find each partial derivative : (a) 8³% дудх2' (b) ეპიც əxəyəz' for z = ln (sin (x − y)). for w=…

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Q: Exercise 8 Form the difference quotient lim h→0 Exercise 9 f(x+h)-f(x) h Evaluate the limit lim (x².…

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Q: Evaluate the limit, if it exists. 1 - 2x² - x4 5+x - 3x4 1 2 (i) lim x → ∞

A: Since you have asked multiple question, we will solve the first question for you as per our guide…

Q: 2ydx + (x x³y³) dy = 0

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Q: Use the graphs for f(x) and g(x) to evaluate the expressions below. Write your answer as a whole…

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Q: Evaluate the definite integral: S." 6 dx

A: This question can be solved using the formula ∫xndx=xn+1n+1+c…

Q: For the function f(x) two periods. Enter the exact answers. 2 cot a determine its stretching factor…

A: We can solve this as follows:

Q: 8. State the domain of the logarithmic function by solving a polynomial inequality. Specify the cut…

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Q: 5. Let w = f(u, v), where u = x + y and v = x - y. Show that дw ди дх ду = () - ( ) 2

A: Given, w=f(u, v) where u=x + y and v=x - y To prove: ∂w∂x∂w∂y=∂w∂u2-∂w∂v2

Q: Consider the following function. g(x) = 3x³ - 8x Find the first and second derivatives of the…

A: Consider the following function.gx=3x3-8xTo find the first and second derivatives of the function.To…

Q: Graph f(x)=3* and g(x) = log 3x in the same rectangular coordinate system.

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Q: Determine whether the sequence is convergent or divergent. If it is convergent, find its limit. (a)…

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