Find the area under the curve y = Find the average value of y = 7x³ over the interval [0, 4]. 7x³ over the interval [0, 4].

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A: Note:- Since you have asked multiple question As per our policy, we will solve the first question…

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Q: P(2,-3,4), Q(4,4,5), T(1,2,7) forms a triangle. find the vector projection of QP parallel on QT.

A: Proj. of QP→ on QT→ = QP→·QT→QT→WhereQP→ = Q-PQT→ = Q-T --------------------------------------------…

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A: domain means value of x which we can put in equation here is in root value cant be less than 0 t -…

Q: rπ/4 x² dx (x²+4)5/2 (Use trigonometric substitution)

A: To evaluate the given definite integral.

Q: Find the limit. NOTE: Enter the answer using round brackets. t² +4 1 = lim t→+∞0 (?, ?) 4t² +5't

A: limt→∞t2+44t2+5, 1t

Q: II. Find Do not simplify your answers. 1. log, (2x² + y) + tan(x − ³) = sin−¹(x² − 1) +

A: Given problem:-

Q: -2 + อน Ore 0

A: Suppose uxy=0 , denotes u = uy implies uy = 0 uxy = F(x) + G(y)  ,satisfies uxy = 0 a) y du/dxdy +…

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Q: b) Determine whether the series n=1 find its sum. Show All Your Work! n-1 (-3)* 4" is convergent or…

A: We need to determine convergence.

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Q: Find Duf at P. NOTE: Enter the exact answer. Duf= f(x, y) = sin(3x – 4y); P(4,3); - = u 3 i

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Q: I. Evaluate the following limits. Using L'Hôpital's Rule is not allowed. - 3. lim 1-3 (x − 3)…

A: limx→0 sin xx =1   and   limx→0 tanxx=1.

Q: Using trigonometric substitution to solve: sin 2x + C 8 cos x√3-cos²x sin 2x 4 cos x√4-sin²x secx 8…

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Q: [2 If A = 3 4 1. 3 2. 6 3. 8 4. 0 x-3 -2 -1 x-27 -1 -5 is a symmetric matrix then x 4

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Q: The IBP formula fudv=uv-fvdu Which of the following statements fits and satisfies the equations? can…

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Q: III. Suppose that a function f(x) satisfies the following properties, together with the table of…

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Q: Solve the given initial value problem. O x¹y² - xy³ = = 84 x³y² - y² = 26 x¹y² + xy³ = 78 x³y² + xy³…

A: Let's find.

Q: Given : x³ sin(2x) dx = 277²-24 Find bif sb . 64 2π 3 5π 6 F|+ =|m 3 3π 4 sbst

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Q: -π/4 x3 dx (x²+4)5/2 (Use trigonometric substitution)

A: We have to solve above question useing trigonometry substitution

Q: 27 If (2x 3) [133] [3] 3] -3 23 1. 2 13 2 2 3. 13 2 23 2 - 0, then the value of x is

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Q: Solve the given differential equation. All solutions should be found. (4y³ + 2x²y) dx - (3xy² + x³)…

A: Use the substitution method and solve the differential equation.

Q: Please solve the problem with complete solution. Thank you

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Q: Use Squeeze Theorem to evaluate lim X→+∞ cos (x) log ₁/2 (x)

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Q: Find the exact arc length of the curvex = 1 3(1² Enter the exact answer. L = + 2)² from y = 1 to y =…

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Q: Solve the given differential equation. All solutions should be found. dy_x³_8y x5 - 8y dx X NOTE:…

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Q: 49-52 Sketch the curve and find the total area between the curve and the given interval on the…

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Q: I. Evaluate the following limits. Using L'Hôpital's Rule is not allowed. (x - 1+1/2/3 1. lim x-1 2x²…

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Q: Let f(x) = 31² - 20x + 25 2x² + 12 - 1 This function has: 1) A y-intercept at the point 2)…

A: Given that    f(x) = (3x2-20x+25)/(2x2+1x-1)

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Q: 60. (a) dx SI dt 1 + √t (b) de fint di dt

A: We can solve this as follows:

Q: dx Arcsin (²) + c

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Q: Determine the number and type of solutions for the equation 4x² +52-5-0 O One repeated…

A: I have appended the formula used in the solution part.

Q: of

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Q: ST/4 x² dx (x²+4)5/2 (Use trigonometric substitution)

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Q: 19 Give the properties for the equation 9x 2 + 16y 2 - 36x + 96y + 36 = 0 Major Axis 8 16 9

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Q: Show that the differential equation xºy7 + x(1+yº)y' = 0 is not exact, but becomes exact when…

A: Take the partial derivative of coefficient of dx and dy to show that the given differential equation…

Q: Using trigonometric substitution, what is sec-1 (-) √x²-9 6x² + C sec (1) √x²-9 6x² + C sec-¹ √x²-9…

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Q: I. Evaluate the following limits. Using L'Hôpital's Rule is not allowed. 3. lim (x-3) tan(9-x²)…

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Q: If f cos42t dt = At - B sin 2t cos 2t + D sin 4t cos 4t + C where A, B, C and D are constants, 2A-3B…

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Q: if any. Find the absolute extremum point(s) of f(x) = el-cost on [−5, π],

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Q: Consider the quadratic function f(z) - 2² +0z + 4. Determine the following: (enter all numerical…

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Q: Find an equation of the surface of revolution by revolving the plane curve 3y = √(9- [(x-1)] ^2)…

A: We need to identify the quadratic surface.

Q: (A) = and B D = . Find the vector projection of A onto 2A - BO O O O none of the above

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Q: Using trigonometric substitution to solve: f cos x dx 3 (4-sin²x)2 11

A: