31. (a) |2x - 1| dx (b) 3π/4 1.T CT/2 \cos x dx

Q: Using mathematical induction. Prove that Ž {i= n(n+1) WHEN 12 1 2

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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, ...…

A: Given ∫cos42t dt=At-Bsin2tcos2t+Dsin4tcos4t+C To Find 2A-3BD

Q: Find the characteristic equation and the eigenvalues (and a basis for each of the corresponding…

A: I am going to solve the problem by using some simple calculus to get the required result of the…

Q: Give the properties for the equation x 2 +y 2 + 4x + 6y - 12 = 0 Domain -3 ≤ x ≤ 8 -5 ≤ x ≤ 5 -7 ≤…

A: We can find the domain of the equation as below.

Q: 7. Do as indicated. 1 1. Let f(x)= = Find the equation of the tangent line to the graph of f'(x) at…

A: This question is related to straight lines, we will solve it using given information.

Q: (D² – D − 2)y = cos x

A: Here is the solution:

Q: fe²x+Inx² sin x² dx = e2x cos x² dx

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

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Q: Use the formula ‹(t) = = 198 t7 k(t) : (4+121 +¹8) ²³/ = ||r' (t) x r"(t)|| r(t) = t²i+t¹¹j X to…

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Q: 23. ["Se' dx 5e* 2 24. S/2 ze de dx 2x

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Q: Find an equation of the plane that contains all the points that are equidistant from the given…

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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: Write an equation for a function that has a graph with the given characteristics. The shape of y =…

A: We can find the correct answer as below.

Q: 2. (D² + 3D + 2)y= 1+ 3x + x²

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Q: IV. Do as indicated. 1. Let f(x)= where z = 1. 1 ²+1 Find the equation of the tangent line to the…

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Q: Identify the center of the conic section whose equation is 4x 2 - 25y 2 - 8x - 100y - 196 = 0. (-1,…

A: We can identify the center as below.

Q: log(x+3) z-1-1-cosh(cos-12) 4. lim

A: Given,            limx→1-log12x+31-coshcos-1x

Q: An object moving along a horizontal coordinate line has directed distance s(t) = 4t³ +9t² - 30t + 5…

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Q: 4x /² sin () cos (+) sin (²) dx (Consider initially the first 2 terms) 3

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Q: Find u v, uu, |v||2, (u v)v, and u. (3v). . u = 8i + j - 3k, v = i - 4j + 3k (a) u. V (b) u. U (c)…

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

Q: Compute the area bounded by the curve x=y²-2y and the line x-y-4-0₁

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

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Q: 2.4 x cos x² dx

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: Calculate[ri(t) r₂(t)] and [r₁(t) × r2(t)] first by differentiating the product directly and then by…

A: This question can be solved using the concept of dot product and cross product of two vectors and…

Q: 7. Determine all relative extrema or saddle points: f(x, y) = 4x³ + 8xy - 2y²

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Q: 1. Evaluate the following limits. L'Hopital's rule is NOT allowed. 4. lim x-∞ 8118 5. lim 1-x+ 2x +…

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Q: Give the properties for the equation x 2 +y 2 + 4x + 6y - 12 = 0 Range -8 ≤ y ≤ 2 -7 ≤ y ≤ 3 -2 ≤…

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Q: Question 2 Consider using the method of partial fractions to solve rb dx = Sa 2x²+2+x³+x² dx = [Aƒ…

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Q: Integrating Factor by Inspection: 7. xdx + ydd = (x² + y²)dx

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Q: Integrate the following functions f(x,y) = 3x-2y. R: over the given regions. the circle x² + y²

A: Given function f(x,y)=3x-2y and region R is x2+y2=1

Q: Determine whether the equation is exact. If it is exact, find the solution. 3 2exycosy + = C 21² 3…

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Q: I-1² ( ²7 ) ₁_²01|1 - 1² || lim, 07

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

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Q: 12. lim [ln(t) sin(t)] t→0+

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Q: f/² sin (1) 4x ; (**) sin (²) COS (²) dx (Consider initially the first 2 terms)

A: ∫vn dv =vn+1n+1+C

Q: Solve the given differential equation. All solutions should be found. dy 3x = e +9y dx NOTE: Use c…

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Q: 15x²x³43x - 19 The integral (x + 1)²(x² - 6x + 13) Ax + B What is the value of dx ? ax²+bx+c 31 -…

A: Given integral ∫15x2-x3-43x-19(x+1)2(x2-6x+13)

Q: ♫/² sin ( cos() sin (²) dx (Consider initially the first 2 terms)

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Q: Write 20 terms of the Fibonacci sequence

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Q: Find a set of parametric equations of the line through the point (1,-2, 3) and perpendicular to the…

A: Given point(1,-2,3) Then the equation of the line passing through 1,-2,3 is…

Q: 1. The following integration can be solved by using the Substitution f 14 dx = ♦ (Choose the correct…

A: use a different techniques to solve this problem.

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: 1 xVx+3 xp:

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Q: Find a power serie CAPS |||| Determine the interval of convergence. (Enter your answer using…

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Q: Select the conic section represented by the equation. 4x 2 - 25y 2 - 8x - 100y - 196 = 0. line…

A: We can answer the question as below.

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

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Q: 2. lim (√x²-x-√x² + x)

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Q: Solve the initial value problem y' = 4 cos(4x) 3+ 2y , y(0) = -1 and determine where the solution…

A: Given IVP y'=4cos (4x)3+2y , y(0)=-1

Q: If y=7x²y+z³ +yz² A = y³ z² e^5x a_x + 4x4 zcosy a_y+ 2x4 CosySinz a_z. Find the following at point…

A: Given, ψ=7x2y+z3+yz2A=y3z2e5x ax+4x4z cosy ay+2x4cosy sinz az           Note: The expert is supposed…

Q: 8 An acceleration function is expressed as a (s, v) = s²-. ' (v+1)³ determine displacement by…

A: a(s, v)=s2-8(v+1)3v(s)=∫0s a(s, v) dv      =∫0s s2-8(v+1)3 dv     =s2v0s -8 (v+1)-3+1-3+10s     =s2s…