Use MUPAD to determine the following indefinite integrals (7.1) (7.2) (2ax-x²)³ dx. S (7.3) Obtain a numerical estimate for the following definite integral Canxi dx. sin x ✓1 + sinx dx

Q: Solve the following initial value problem: y(t) = = dy dt +0.9ty = 6t, y(0) = 1

A: Given: dydt+0.9ty=6t,      y0=1

Q: The curve y = ax³ + bx² + cx + d has a critical point at (-1,3) and has a point of inflection at…

A: We are asked to which is true for the given condition  Note: Critical points are points where the…

Q: 3x²-2 do 3 2x - 4x

A: Here we will solve the given integral,

Q: Find the gradient of the function at the given point. Function Point (3, 7, 2) f(x, y, z)=√√√√x² +…

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Q: Write the first five terms of the geometric sequence. a 1 =  -5; r = -3

A: We can find the first five terms as below.

Q: Which of the following is a valid triple integral? ⒸSS ſo ſh(e) (5) f(x, y, z) dzdydr h(y,z) flus) f…

A: We have to discuss about valid triple integral.

Q: If then fyy = Select one: O True O False f(x, y) = 2(x² + x) (x - y)³ x² + y x - y

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Q: Suppose that f is a differentiable function with f(2) = 5. If the tangent line to the graph of y =…

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Q: Given the system x + 3y = 10 2x - y = 6 a) Create the augmented matrix of the given system b) solve…

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Q: Evaluate: 12+3 2√x+3 ○1-3 ln (7/5) O2-3 ln(7/5) 2 O2+3 ln7 03-In()

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Q: Evaluate: cot (9) -do None of the choices ɔ+ − ( 7 ) 400 - ( 7 ) 8400 O tan³ () – tan an ( 1 ) - + +…

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Q: Determine a suitable form for Y(t) if the method of undetermined coefficients is to be used. y(4) +…

A: We have to find the suitable form of Y(t).

Q: Present a second order differential equation. Identify the corresponding auxiliary equation.…

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Q: If f'(1) = 4, f(1) = 2, and g(x) = f(x) tan-¹x, what is the slope of the tangent line to the curve y…

A: Here we have to find the slope of the tangent line.

Q: a b) exist. x² yesy 8x4+7y² Find the domain of the function f. f(x, y) = Show that lim f(x, y) does…

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Q: lim cot 1 -1 8418 1

A: A detailed solution is given below.

Q: Find 7 sin (7x) dx

A: According to question,Given Integral,Let I = ∫7 sin27x dx

Q: Find a normal vector to the level curve f(x, y) = c at P. X = x² + y² P(5, 5) f(x, y) = C = 100

A: To find the normal vector.

Q: A graph of a model for the sales of services between 2004 and 2008 by a leading global provider of…

A: We have to find the solution of given question.

Q: f(x, y) a b) = 4x²+2y² Find the domain of f. Show that the limit does not exist lim f(x,y) (x,y) →…

A: Here, the given function is: f(x,y)=3xy4x2+2y2

Q: Evaluate S ○ In O Divergent ○ In 11 ○ 6 In 11 6 dr 2²-25 16

A: We need to evaluate integral.

Q: If z = √√√xy, dz and x = t², y = 1² then =? dt Select one: O √xy(21) O √xy(21²) 0 2t O None of them…

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Q: if z=xarctan(y/z), find ∂z/∂x at x=0, y=1, z=1

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Q: (zin z + 5)dz

A: The given integral is [xlnx+5] limit from 1 to 3.

Q: given z=xlny-((2^x)/y)+ysinhsqrtx, find (∂^4)z/∂x∂y∂x∂y

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Q: π/2 The integral f/2 So sin drde is equal to cos O-1/2 O 1/2 0 1 00 10

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Q: then the / r(t)dt is equal to r(t) = (-2 cos (21), 3 sin (4t), In (2t)), Select one: True where C is…

A: Please see the below picture for detailed solution.

Q: find the rate of change of the circumference of a circle when the area is increasing at the rate of…

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Q: A movie theater has a seating capacity of 163. The theater charges $5.00 for children, $7.00 for…

A: A detailed solution is given below

Q: Question af If f(x, y) = xy² - x ln(y) find Ət if x(t, s) = s² - st³ and y(t, s) = e-st²

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Q: Evaluate: f³² ƒ³³ fő cos(# ) dzdxdy J(ㅠ-2) ○ 4 (ㅠ-2) ○ 4m ㅇ 풍 4

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Q: Find the normal vector to the level curve f(x, y) = c at P. f(x, y) = 6 - 4x - 7y c = 6, P(0, 0)

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Q: graph 10 5 0 answer 5

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Q: Given y = cos(3x), find O O 3 2- * N O √3 3√3 dy at x = 5

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Q: increasing decreasing f(x) = sin(x) + 1 T 2 + πn,∞0 0 < x < 2π (-∞0, 1/2 + 1) X X

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Q: Use the Comparison Test or the Limit Comparison Test to determine whether the following series…

A: We need to choose correct option.

Q: Question 25 A function has a relative maximum if O The first derivative test shows that the slope of…

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Q: A road perpendicular to a highway leads to a farmhouse located a = 1.5 km away. An automobile…

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Q: Question a) b) Let f(x, y) = 2√x - y²e-²xy + ²². Find fx and fy. Evaluate fxxy(4,-1).

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Q: Find the limit, if it exists, or show that the limit does not exist. x² - 3y² lim (x,y) (0,0) x² +…

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Q: dz Evaluate: 5 10+2% 0 1 O Divergent 00 0-1 15

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Q: Region A is bounded by the parabola x = y², the line y = 1, and the y-axis. Region B is bounded by…

A: As per the instruction, we will be answering the first question. Given: We need to find the volume…

Q: Which of the following is the partial derivative with respect to x of the function f(x, y) = 2y sin…

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Q: Find y': Oy: Oy = Oy' = O y' y cos(xy)+1 x cos(xy)-1 x cos(xy+1) y cos(xy)-1 y cos(xy)+1 x cos(xy)-1…

A: To find the value of y' for the given function.

Q: Find the gradient of the function at the given point f(x, y) = 5x + 4y² + 1, (1,4) Vf(1, 4) =

A: Solution of given question is written in below steps.

Q: b) Evaluate lim X-8 In(5x) In(2x-4)

A:

Q: Find the limit of the following sequence or determine that the sequence diverges. (-1)^) 4n+3

A: The given sequence,       -1n4n+3

Q: √x +3 If f(x, y) = xy + 7 the domain of f(x, y). Select one: True False then the point (1, −7) is in

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Q: Find a parametric description of the line segment from the point P to the point Q. P(0,0), Q(22,-26)…

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Q: a, b, and I are differentiable functions of the same variable what is the derivative of H ac b +…

A: To find the derivative of acb, here a,b and c are differentiable function of same variable. Let a,b…