Evaluate the following integrals: dx dx ·S b. S √81+16x² √16x²-9 a. dx 49-4x² c. S.

Q: Identify the theorem: If S is the boundary surface of a solid E in 3-dimensional space, then SS, F.…

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Q: The function 5x+1 f(x) 1-In (x³ +e) has a Maclaurin Expansion O false O true

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Q: Find the area bounded by the curve y = 4+2x+z² and x-axis from z=-3 to z = -1. Area of the region -

A: y = 4 +2x + x2 A =∫-3-1f(x)dx A = ∫-3-1 4 +2x + x2dx A = [4x +x2 +x3/3]-3-1 A = (-4 +1 -1/3) - (-12…

Q: O The series Σ7-"[2 +5¹] n=1 converges to none of the choices the above converges to converges to…

A: The above series converges to

Q: Determine the equation of the hyperbola with center (−1, –4), a focus at (−11, –4), and a vertex at…

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Q: A particle is moving along the path given by R(t) = (sin(ln t), cos (Int), √3 lnt). (a)…

A: Let's find.

Q: 6. Evaluate J-csc(x) cot(x) dx O cot(x) + C O csc (x) + C O-cot(x) + C O O O O Cannot be found

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Q: Identify the theorem: If C is the boundary curve of a surface S in 3-dimensional space, then the…

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Q: Evaluate the integral. π/4 Jo 0 sin5(x) dx

A: Given query is to find the value of the integral.

Q: log3 = X-1 3 √3-2x

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Q: Calculate the integral approximations Tg and Mg for (lnx)-¹1 dx. Your answers must be accurate to 8…

A: Given problem:-

Q: Set up the definite integral required to find the area of the region between the graph of y = 12-2²…

A: we have to find out area

Q: Determine the equations of the tangent and normal to the curve y=2xex at (0,0)

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Q: 7 13 8 a Find the area of the shaded region above.

A: Since you have asked multiple questions in a single request we would be answering only the first…

Q: Find the maximum and minimum values of the function f(x, y)-xy subject to g(x, y) = x² + xy + y² =…

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Q: 8 Find the area bounded by y=-, y = 2x, y=0 and x = 3. X Using vertical element, what is the…

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Q: Write an equation for the transformed logarithm shown below 5 4 3 2 1 -5 -4 -3 -2 -1 3 4 5 f(x) = N…

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Q: A company produces a special new type of TV. The company has fixed costs of $461,000, and it costs…

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Q: Write TRUE or FALSE before each statement. Solve yy= - dependent variable. Statement 1. The…

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Q: Find all the values of x such that the given series would converge. 8 8n (x²)(n+1) (n+8) n=1 The…

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Q: Find the curl of the following vector field: F = (z, 2y, -3x)

A: Follow the procedure given below.

Q: Determine the equation of the ellipse with center (-2,-4), a focus at (-2,5), and a co-vertex at…

A: Given:        center =-2,-4        focus =-2,5        co-vertex 10,-4 Equation of Ellipse is…

Q: A balloon is rising at a rate of 3 meters per second from a point on the ground 55 meters from an…

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Q: Use a product-to-sum formula to convert the expression to a sum or difference. Simplify where…

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Q: Evaluate the double integral over the given region R. S xy cos y dA Sfxy |xy cos y dA= R: -1≤x≤1,…

A: NOTE: Refresh your page if you can't see any equations. . the given integration is  the limits of x…

Q: For which of the following does the Mean Value Theorem apply? TT a) f(x) = tanx, - ≤x≤I b) f(x) =…

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Q: The components of vectors A and B are given as follows: A=5.1, A = -5 X y B-2.6, B = -4.3 X y What…

A: We have to find magnitude of vector sum A+B.

Q: Using an appropriate substitution | tan³x sec7xdx is equal to

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Q: What is an equation for the cosine graph shown below? -135 -90 -45 -11 -10 +9 8/ -7 -6 -5 3 2 1 45…

A: Given query is to find the cosine equation of the function.

Q: 2. Determine the angle, to the nearest degree, between the vectors * = (4,6,-2) and y = (1,8,2)

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Q: Find the derivative of V(x) = ln(sin x) – (x4 – 3x)10

A: We can find the derivative as below.

Q: Q3: A. By power series, prove that: d 4 sinhx dx coshx

A: Explanation of the answer is as follows

Q: The table shows values of a force function f(x) where x is measured in meters and f(x) in newtons.…

A: Here, the work done is given by: W=∫018f(x) dx

Q: The Taylor series for f(x) = e at a = 1 isen(x − 1)". - n=0 Find the first few coefficients. CO C1 =…

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Q: 6 300 m 10. Cleatus, owner and operator of ACME Golf Inc., has a scheduled appointment at…

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Q: Apply the definition to differentiate the following functions: 1- y = ₁

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Q: Lim x-0 et +ex -x²-2 sin² x-x²

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Q: There are two extremely important sequences that we will discuss in this chapter: arithmetic…

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Q: A frozen turkey comes out of the freezer at 0°F and is placed in a refrigerator that is set to 37°F.…

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Q: Find the parallel projection of the vector v = onto the vector w=.

A: Given problem:- Find the parallel projection of the vector v=<4, -5, 7> onto the vector…

Q: Assume that the vectors a, b, c, and d are defined as follows: a = (8,3) b = (6,5) c = (4, -1) d…

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Q: Find the interval of convergence for The interval of convergence is a E n=1 (x - 1)" n 3n

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Q: 2. Water leaks from a tank at the rate of r(t) gallons per hour. The rate decreased as time passed,…

A: solution:-left end pointRiemann sumnumber of rectanglen=5∆t=10-05=2t0=0, t1=2,  t2=4,  t3=6,  t4=8,…

Q: need

A: We will solve the problem

Q: Q2: Find the determinant of 3x3 Matrix. 5 7-8 4-36 1 7-9

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Q: Find the transition points. f(x) = x(11-x)1/3 (Use symbolic notation and fractions where needed.…

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Q: LAW OF GROWTH AND DECAY A bacteria culture increased 800% in 1 year. How long (in months) will it…

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Q: Suppose that f(4) = 2 and f' (4) = -1. (a) h(x) = (2x². 2x² + 31n (f(x)) h'(4) = (b) h(x) = 20f(x)…

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Q: B. For the figure shown below, find the sum of the areas of all the semicircles. 244

A: Using formula of area of circle

Q: Find Hence evaluate d dr 1 Š S ₁ (1 +2²2)³/26 0 -1 1+x², dx.

A: