Consider the matrix A= Calculate a31 Calculate 932 755 826 5 2 6 e 9 dh n bf a

Q: √√√x- S: z 12, x² + y² ≤ 1 Evaluate (x - 2y + z) ds.

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Q: Let R be the region enclosed between the curves r²=y-1 and y=5. Sketch R and find its area.

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Q: Let E be the solid below z = 50- x² - y² and above the square [-5, 5] × [-5, 5] Given the solid has…

A: Let's find moment of inertia of E about z axis.

Q: · (b + c) = ² 7. Prove that à. = a · b + ac for all a, b, c € R³.

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Q: Determine the open intervals on which the graph is concave upward or concave downward. (Enter your…

A: We have to find open intervals on which the graph is concave upward or concave downward

Q: Find the acceleration vector for the position vector r(t) = (sin(11t), 4tº, e -2t). x component = y…

A: We need to find acceleration vector.

Q: m M|L II k=0 CO M« Σ N சிய

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Q: Det er mine absolutely it each convergent, Conditionally convergent, you > k=1 the following is or…

A: Given ∑k=1∞coskπk

Q: , b) Find the angle ZB.

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Q: If an > 0 and an converges, then (-1)"an converges. Select one: O True O False

A: Absolute Convergence test :The absolute convergence test states that, If ∑n=0∞anconverges then,…

Q: Assume that the temperature of a person during an illness is given by: T(t) = 8t/t^2+7 , where T is…

A: The answer is given in step 2.

Q: у 7. y' +²√y = 0, y(1) = 0 - x

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Q: Find the point at which the line y(t) z(t) = 2 + 4t -6-8t intersects the yz plane. 6-7t

A: The line x(t)=2+4t, y(t)=-6-8t, z(t)=6-7t intersect yz plane Note:    Multiple questions are given,…

Q: Solve (2y² + 3xy a. - 2y + 6x) dx + x (x + 2y x² (y² + xy + y + 2x) = C b. O c. x² (y² + xy y² (y² +…

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Q: Problem Set question: The position function for a falling objects is given by s (t) = -16t² + vot +…

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Q: sinh³ (x) cosh (x) dx =

A: we have to evaluate the integral ∫sinh3x cosh8xdx use the formulas,…

Q: 1 4. f₁² (1-x²) dx 5 2

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Q: What are two numbers whose sum equals to 23, and whose product is a maximum

A: Let the two numbers be x and y.

Q: 1. Which of the following relations is a function? a) {(1,9), (2, 4), (2, 3), (4, 15)} {(2, 7), (7,…

A: Recall:  A function can be defined as a relation between "each of its inputs" to "exactly one…

Q: (a) Find the velocity function. v (t) = (b) Find the acceleration function. a (t) = PY PW POY

A: A particle moves according to the position function st=e4tsin5t To find the velocity and…

Q: Let the line PQ pass through the points P = (-4,-4, -6) and Q = (-2, 1, - 16). The line will pass…

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Q: Find the area of the region between y = 6x² and y = x² + 7.

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Q: Let f(x, y) = 2e sin(4) of д х of dy Check Answer

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Q: 1 6. √₁² √ 1 - √u du

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Q: e) 3 (12x²-108) 2 x + x - 12

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Q: Find the average value of the function over the given Interval. (Round your answer to three decimal…

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Q: 2. Captain Crunch wants his airplane to travel along a path that is [N60°W] with a groundspeed of…

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Q: 2.fe-2y dy

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Q: A tank half-filled with water is in the form of a rectangular parallelepiped 5 ft deep, 15 ft wide,…

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Q: If u = sin® 3 - x 2 find Ou Əx Ou and ह Hence show that 2 Ou 1 y x 3 –x dy Ou = 0

A: Given u=sin-13-xy2

Q: Find the Indefinite Integral and check your result by differentiation. (Use C for the constant of…

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Q: 2. Consider the parallelogram ABCD where A(0,1,2), B(1,2,3), and C(0,3,5). [2] a) Find the…

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Q: Find the Maclaurin series for f(x) using the definition of a Maclaurin series. [Assume that f has a…

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Q: dr Let A be the area of a circle with radius r. If dt = 2, find dA dt when r = 4.

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Q: 9. Compute the area of the region in the ry-plane wich is bounded by the z-axis and the curve r(t) =…

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Q: Question 2 Compute the following limit. Give your answer as a simplified radical, if necessary. lim…

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Q: Find the tangent plane to the equation z = - 3x² + 2y² + 4y at the point (4, 1, - 42). 2 = Check…

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

Q: Which of the following is the complete set of roots of the auxiliary equation fory"'' - 3y "' + 3y…

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Q: Use Taylor series you already know to find the Taylor series generated by f(x) = x sin(6x) at x = 0

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Q: Evaluate the limit. Note: Enter two 'o's to make infinity (oo). 1 [ In(t-2) lim e³-t Check Answer

A: Given problem:- limt→∞4t,e3-t,1lnt-2

Q: Basic Level 1. The graph shows the total cost of making compact discs. 250 Namibian Dollars…

A: According to the graph :-cost of 0 compact disc=N$50 thousandscost of 5 thousands compact disc=N$80…

Q: Which of the following is a linear differential equation? O da-t{1+t²) sec² ædt = 0 O…

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Q: Define g(x) to be the restriction of f(x) to the largest possible domain containing x=0 so that g(x)…

A: We have given f(x)=x-12+2You asked to solve only part(b). So we will solve part(b)In part(b) we have…

Q: Evaluate J 2xz dV where E = E Round your answer to four decimal places. {(x, y, z) | 2 ≤ x ≤ 5, x ≤…

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Q: If f(x) = (t + 3)e' dt, on what interval is f increasing? (Justify your answer)

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Q: A tank half-filled with water is in the form of a rectangular parallel piped 5ft deep, 15 ft wide…

A: Answer is c

Q: Question 1 Find lim f(x) given the graph of f(x) shown below. x-5 +++ -10-9-8-7- Y 3 4 5 6 7 9 10 x

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Q: (−4 − x)² +5 if x ‡ − 5 Let f(x) 4x + 25 if x = -5 Calculate the following limits. Enter "DNE" if…

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Q: If 0 ≤ an ≤ bn and bn diverges, then an diverges. Select one: O True O False

A: This question is related to series and sequence, we will solve it using given information.

Q: Evaluate (2 - xy) ds where C is the curve given below. -2 -1 -2

A: Given   ∫C2-xyds Curve C