Express the integrand as a sum of partial fractions and evaluate the integral. 22dx S 2 x²-1

Q: a) Let zi = 4 cos Find 2₁ - 22 and 7π 12 21 Z2 5TT 12 + i sin and = 3 (cos. Leave your answer in…

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Q: We start from the expression for the contact force 4 a³ 1/21 F=E (₁ 7² - (07*³²¹) ³²) '8γπa3 E* 3 R…

A: We have to find the differentiation of the above equation.

Q: Please fix the mistakes that are in Red for me.

A: topic - application of derivatives

Q: Consider the following double integral - f By reversing the order of integration of I, we obtain:…

A: We have to reverse the order of given integral

Q: ★ Each series converges. Show why, and compute the sum. k Σ[-88-(-3)*] k=2

A: p

Q: S x-6 x²+9 dx

A: To evaluate the given integral. ∫x-6x2+9 dx

Q: dx ylnx- dy y + 1₂ X 2

A: given :ylnxdxdy=y+1x2

Q: Given the graph of the function y = f(x) below, identify which of the following statement is/are…

A: The limit definition of derivative of a function at x=a is given by  f'(a)=limx→af(x)-f(a)x-a. For a…

Q: a) Use the Quotient Rule to find the derivative of the given function. b) Find the derivative by…

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Q: Suppose x = ₁et + c₂e³t. a. Verify that x = =c₁e¯t + c₂e³t is a solution to x" — 4x' - 5x = 0 by…

A: Topic = Differential equation

Q: A cubic block of ice whose side is 2 inches long is melting at a rate of 1 in³ per minute. How fast…

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Q: Find the critical points c for the function f and apply the Second Derivative Test (if possible) to…

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Q: Use symbolic notation and fractions where needed.) a= b = C = d =

A: Topic:- calculus

Q: B-Soive the Differential equation : Y 1 x√√x+x = 0, y(9)=1.

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Q: 2. On the wall of Mr. Piamonte's house, a 6 meter picture was hung so that its location is 5 meters…

A: 2.

Q: √₁² x (1 – x²) dx

A: Topic = Integration

Q: Directions: Using Fundamental Theorem of Calculus (FTOC), compute the following definite integrals.

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Q: (E) List the values of all local minima of f(x). If there are no local minima, enter 'NONE'. x x…

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Q: Determine if 1781 is divisible by 3, 6, 7, 8, and 9.

A: Determine if 1781 is divisible by 3, 6, 7, 8, and 9

Q: Use the four-step process to find f'(x) and then find f'(1), f'(2), and f'(3). f(x) = -x² + 3x - 6…

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Q: 3. Sketch the graph of one function f(x) that has all of the following properties: a.) The domain of…

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Q: Find the derivatives of the given functions using the rules of differentiation. 1. Supposed that you…

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Q: The average rate of change of f(x) = cos(x) with respect to x as a changes from 0 to π is 2 OOO 2 -2…

A: We have to find the average rate of change.

Q: S 10dz 4z³-4z² + 5z

A: We have to find value of given Integral using partial fraction.

Q: Apply the second derivative test to find all relative extrema. (c) f(x) = 1

A: To find the relative extrema first we  find the critical points. The critical points are the values…

Q: Q3/ Evaluate four of the following integrals. ( x³+1 sinx cosx dx b. f*+¹ dx c a. S √1+cos2x x²

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Q: Consider the following matrices: [2 3 id -1 27 - - A = B = 3 0 C = 1 0 b 4 1 Perform the following…

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Q: 6. Evaluate In (x - In (r-...))dr in terms of some new variable t (do not simplify).

A: Given :- ∫ ln(x-ln(x-.....) dx in terms of some new variable t

Q: dy II. Use the Inverse Function Rule to find (show your complete solution) dx 1. x = y + y² + y³

A: Given

Q: Is it possible to Solve all the points with finding Domain and Range. 1) y sin x y = cos x y= tan x…

A: As per our company guidelines we are supposed to answer only first 3 sub-parts. Kindly re-post other…

Q: 2 y = 3x³+=+6x X

A: We use the formula as given below:

Q: Ут. У 4+ 2 ly мв a.

A: The given series,       ∑k=1∞2k4+k

Q: Find the absolute maxima and minima of the function on the given domain. T(x,y) = x² + xy + y² - 9x…

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Q: 9. (20 pts) Find the area between (bounded) by the curves y = x² + 10x and y=2x+9.

A: Given: curves y=x^2+10x , y=2x+9 We have to find the area between the curves

Q: If you evaluate the integral expression |2x-1|dx the result is Blank 1 (use fraction or decimal in 2…

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Q: 2) Find the average value of the function f(x, y) = 6x + 4y over the plane region R. defined by the…

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Q: Find equations of the line through the point (1, −1, 1) perpendicular to the line 3x = 2y = z and…

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Q: in how many ways can we arrange the integers 1, 2, 3, 4, 5 in a line so that there are no occurence…

A: We use the principal of inclusion and exclusion.  For i∈1,2,3,4, let Ai ⊂Si be the set of all…

Q: 6 Consider the three by three system of linear equations 2x + Y + + 2y + 2z 5z 12. We will solve…

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Q: Find all critical points of f(x) = 3 + 12x - x² and use the First Derivative Test to determine…

A: Given function f(x)=3+12x-x2 To find critical points we need to differentiate the function f'(x)=0…

Q: 3. Let there be some a, b ER such that f(a)f'(a) = f(b) f'(b) + 1. Show that f f(x)f"(x)dx ≤ 1.

A: This is a problem related to integration. Based on the general formula and concept we will prove the…

Q: 7. (10 pts) Evaluate the integral Sa x4 6x5 - 1dx

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Q: (a f (x) + b g(x)) '= a f (x) + b g'(x)

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Q: Find the area of the region bounded by the graph y = sin x, y = 0, x = 0 and x =3π/2

A: Area of a region when strip taken parallel to y-axis is ∬dydx.

Q: Find the volume of the solid generated by revolving the region bounded by y=3/(2√x), y=0 & 1s XS4.

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Q: Which value of c satisfies the conclusion of the MVT for the function f(x) = -6x²-3x - 2 on the…

A: Solution-

Q: 16) Compute the first and second-order partial derivatives for f(x, y) = x²y³ + x + y² − 3

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Q: 3- Find the length of the curves in Exercises 1-4. x = = (y3/2/3) - y¹/2 from y = 1 to y = 9

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Q: Determine the intervals on which the given function is concave up or concave down and find the…

A: The graph of  y =f(x) is concave up on those interval where f"(x)>0 . The graph of  y =f(x) is…

Q: SUBJECT

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