III. Partial Fraction Decomposition: Evaluate the following integrals using partial fraction decompo- sition. 2. 1 r²(x-1) dz

Q: Question 3 For the function below, how many regions are at least needed to facilitate the tracing of…

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Q: Find the critical numbers of the function. (Enter your answers as a comma-separated list. If an…

A: Given

Q: 1. Find each of the following derivatives. d a. dx (4 sinx) b. [ln (2x4 - 3x)]

A: We have to find derivative of given function.

Q: Let P be the set of points that belong to the shaded region imaginary The set P is (A) open (B)…

A: We can see that the outer boundary is not included in the region. So set is not closed.  We can see…

Q: hid. The line y d. The line y = -5/8 -5/8 redbuthents 2 y 0 X = ochiul 14 4 X = - y² 2 1 y² dibel 2…

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Q: 6. Find the radius of convergence and the interval of convergence for E-0¹ (x-2)".

A: 6. The given power series     ∑n=0∞12nx-2n

Q: Find the orthogonal projection of b = [4 2 -4] onto the column space of the matrix A. (Enter each…

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Q: A region bounded by f(x) = x², y = 0, and x = 4 is shown below. 2 Find the volume of the solid…

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Q: (7) ² Fi²+ Fi²+ ² Fi Fz Cos/20 49=F₁²+ F²-FiFe- tan 8= 48- = 4√3 4√3= F₂S in 190 Fit F₂ Golze $7…

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Q: Question 4. Determine if the series Σ n=1 5n+1 7-2 converges or diverges. If the series converges,…

A: We have to find the given series is convergent or divergent  , if the series is convergent give its…

Q: c. Given f(x) = 2x - 3, g(x) = -4x² +9, h(x) = 4x² - 12x +9; find f(x)* g(x) 2. h(x)/ f(x) 3.…

A: Given, f(x) =(2x-3) g(x) = -4x2+9 = 9-4x2 = (3)2-(2x)2 = (3-2x)(3+2x)  h(x) = 4x2-12x+9 =…

Q: let a=2+7i b=4-2i Choose the correct result of a*b* O 24+22i O22+22i O22+241 O 22-24i

A: Given that a = 2 + 7i and b = 4 - 2i. We have to find a*b. Clearly as  a = 2 + 7i and b = 4 - 2i so…

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

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Q: Ju 2²u Consider the heat equation = Ət for a bar of length L=1, with non homogeneous boundary…

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Q: For the function f(x) = 2x2 - 5x a) Find f'(x) from FIRST PRINCIPLES b) Use your result from a) to…

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Q: 4. Given cos 2x = cos²x - sin² x. (Optional) (a) Verify sin 2x = 2 sin x cosx. cos 2x, (b) Express…

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Q: Sketch the graph of f and use your sketch to find the absolute and lo f(x) = sin(x), 2 absolute…

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Q: Given f(x) = 3x+8, (a) Find f(x+h) and simplify. (b) Find f(x+h)-f(x) h Part: 0 / 2 Part 1 of 2 (a)…

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Q: Find the derivative of the following function. Factor fully and simplify your answer so no negative…

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Q: 1 f(x) = X g(x) = Inx A) In[f(x) + c C) Inf'(x) + c 1 1+2e-x A) In|1+2e C) Inje*+1| + c 5. f(x) g(x)…

A: We can answer both the question as below.

Q: The velocity function is v(t) = t2 - 4t+ 3 for a particle moving along a line. Find the displacement…

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Q: Use the method of reduction of order to find a second solution of the differential equation ty" +…

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Q: ror(4)). 95. Find the restrictions in the domain, if any, for If there is more than one restriction,…

A: Note: The first question that is question 90 seems incomplete. So, solving 95 for you.

Q: Suppose that the nth term of the sequence of partial sums for a given series is Sn = 1+2n+3n² 4n²…

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Q: (a) Assume that f(x, y, z) and F(x, y, z) are arbitrary differentiable functions such that f(x, y,…

A: Given

Q: A 30 6 12 ♡ E C D F Find the area of Square ABCD

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Q: 14. Integral 2 dt 31-4

A: Given, ∫23t-4dt

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Q: Find the area between f(x)=x²-12 and the x-axis from x = 0 and x = 2. The area is square units. ...

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Q: If f f(x) dx = 3 and I. III. [f(x)g (x)] dx = −6 III only I, II and III I only O II only g(x)dx =…

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Q: If f(x) dx = 3 and g(x)dx = −2, then which of the following must be true? I. f(x) > g(x) for all a ≤…

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Q: 1 3x (2x + = + ₁). x+1 Find k'(x) if k(x) = 3x (2x + Provide your answer below: k'(x) =

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Q: If f is the function given by ƒ(x) = √²* √t² — t dt, then ƒ' (2) = 7 a. 2√12 b. √2 c. √12 d. 2√12 B…

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Q: A region bounded by f(x) 8 7 6 Find the volume of the solid formed by revolving the region about the…

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Q: d²y dx² dy dx -+ 2y = cos (e-x)

A: The given differential equation is;  d2y/dx2-3dy/dx+2y=cos(e-x).

Q: Using the Limit Laws, find limt→0 t2+9−3t2. Do not use L'Hospital's Rule.

A: By using the Limit Laws, to find limt→0 t2+9-3t2.

Q: Use the matrices below to perform the indicated operation if possible. 6 B-[-3.0-[1] C [89] -4 = If…

A: Performing the indicated matrix operation

Q: 15. integral sin 4x cos 4xdx

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Q: In a circumference of radius r (in meters), its radius increases at a rate of 2.8 meters per hour.…

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Q: Given the functions: g(x) = |x-2| Evaluate the function (h-g) (5) for the given value of x. Write…

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Q: Determine the longest interval in which the given initial value problem is certain to have a unique…

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Q: Solve the given differential equation. 16x2y" + 16xy' - y = 0 C₁ cos(In(x)). + C₂sin (In(x)) 4 4…

A: here we have to solve differential equation.

Q: Using the Inverse Function Theorem, what is (-1) (8) given that (x) = √6x-2? Note that (11)= 8. (Do…

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Q: dz - 6² 7 4 16 + Consider the integral 7² +16 du ONI - S = (2-16) a) I= /0 du O b) I 117 So u (u -…

A: Given :I=∫01dz7z+16

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A: Here, the eigenvectors corresponding to λ=-3 is 011

Q: An airplane is flying at an elevation of 5150 ft, directly above a straight highway. Two motorists…

A: To find the distance between the two cars.

Q: 1. The radioactive isotope hydrogen-3 has a half-life of 12.3 years. a. If a sample of 80 mg of…

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Q: f(x)=5sinx+2cosx,on(−π,π)f(x)=5sin⁡x+2cos⁡x,on(−π,π) a) Determine the intervals on which ff is…

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Q: the complex number 6√3+6i in polar form O 12(cos(n/6)+isin(n/6) O 12(cos(n/4)+isin(n/4) O…

A: As we know that; The complex number z=a+ib can be written as polar form; z=rcosθ+isinθ Where;…

Q: 4: Find the indefinite integral of f(u) = -1-3√ =

A: