1. 2y7y"+12y + 8y = 0

Q: Suppose f'(a) exists for all a in (a, b). Mark all true items with a check. There may be more than…

A: This question can be solved using the concept of continuity and differentiability in an interval.

Q: (B) Use Tabular integration to evaluate the following: - f(t³-4t² + 5t + 32) sin(t)dt

A: We can evaluate the given integral by using the tabular integration.

Q: (b) ₁₂ (x − 1)(x + 2) de L dx - -2

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Q: 1.₁-1/dt 2. -1 -2es-1ds

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Q: Find the derivative of the following functions by using the limit definition of the derivative.…

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Q: 2. Let f(x) = 24. Sketch the graph of f(x) on the graph below. Then use the graph to find the…

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Q: Use Newton's binomial theorem to calculate √50 with 4 terms.

A: You have submitted multiple questions. According to Bartleby guidelines, I'll solve the first…

Q: (B) Use Tabular integration to evaluate the following: - f(t³-4t² + 5t+ 32)sin(t)dt

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Q: anchor 1, anchor 2 One of the guy-wires forms an angle of a = 0.3 radians with the antenna and the…

A: Let's solve part d and e.

Q: Q2: dy du (A) Show that if y=csc(u), then -csc(u) cot(u) dx dx

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Q: = 0.3t centimeters per minute 2. The depth of the water in a tank is changing at a rate of r(t) O,…

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Q: Let F be the function below (Click on graph to enlarge) Evaluate the following expressions. Note:…

A: limx→a F(x)=L if and only if limx→a+ F(x) = L= limx→a- F(x) . A function F(x) is continuous at x=a…

Q: The director of the school play has to assign 5 lead roles. If the roles are being chosen from a…

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Q: to evaluate the following: f(t³-4t² + 5t+ 32) sin(t)dt (B) Use Tabular integration

A: Given integral is :

Q: (B) Use Tabular integration to evaluate the following: - f(t³-4t² +5t + 32) sin(t)dt

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Q: (B) What function f(t) has Laplace transform: f(s)= s² + 1 s(s+s-12) 12

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Q: y = 7+1-y, y(0) = 1 (a) Find approximate values of the solution of the given initial value problem…

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Q: Q16) Find the value for a,b. it f(x)= ax +4x²+bx has stationary point at x1, and inflection point at…

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Q: What is the 100th term of the sequence –3, 2, 7, 12, ...?

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Q: Given the vecor-valued function R(t) = cosht i ln(t+1) j+et k, find lim h→0 R(0+ h) - R(0) h O…

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Q: Find all solutions of the equation in the interval [0, 27). 2 cos 0+1=0 Write your answer in radians…

A: Given:   2cosθ+1=0   2cosθ+1-1=0-1             {subtract 1 from both sides}   2cosθ=-1   2cosθ2=-12…

Q: A rectangle has a perimeter of 120 meters. What dimensions yield a maximum area? Let the domain of…

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Q: Fill in the blank. (Note: The notation x→ c' indicates that x approaches c from the right and x → C…

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Q: Set-up the double integral for the area of the region outside the unit circle r = 1 and inside the…

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Q: (B) let y = 3sin5x-2cos5x show that y + 25y = 0

A: Given :y=3sin5x-2cos5x    To prove : y''+25y=0

Q: 17 Evaluate the integral: SERV - dx x²√x² + 25 (A) Which trig substitution is correct for this…

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Q: Use mathematical induction to prove the following: 1 + 3 + 5 + ... + (2n – 1) = n² for n ≥ 1

A: This question can be solved using the four basic steps of mathematical induction.

Q: AY (1, 1) A X=1 y=x² с X (0,0) = 1, and the y-axis. Region A is bounded by the parabola x = y², the…

A: Note : As per our guidelines we are supposed to answer only 3  subparts if there are multiple…

Q: Find the area of the surface obtained by rotating the curve from x = 0 to x = 5 about the x-axis.…

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Q: Suppose the labor cost (in dollars) for manufacturing a camera can be approximated by 3 L(x,y) = x²…

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Q: 5. 6. tan x dx \cos x (1/2-√√x) dx HIM

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Q: An object is moving with velocity (in ft/sec) v(t) = t²-2t + 3. At t = 0, the object has a position…

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Q: Solve for x = u + 1 and y = 2u² - 4u d²y dx² with respect to the parameter u

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Q: Use Taylor's Theorem to find an interval [ z, z] where the Maclaurin polynomial p2(x) = 1- 2 1…

A: Given problem  is :

Q: Find the length of the curve Arc length = UT → y² = 4x, 0≤ y ≤ 2.

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Q: Write out the first four terms of the Maclaurin series of f(x) if f(0) = -9, f'(0) = -9, f"(0) = 2,…

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Q: 5. (a) Use Newton's binomial theorem to calculate √50 with 4 terms.

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Q: Find all the relative extrema and saddle points, if any, of the given function below: f(x, y) = 18x²…

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Q: Find the arclength of r(t)= on the interval from t equals zero tot equals 2 times pi.

A: Given:  r(t)=<5cot(t), 3 sin(t), 4 sin(t)>To find:  Arc length form t=0 to t=2π

Q: x2 (C) S²_₁₁√x+2 -1 dx

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Q: -. Find the area of the region between f(x) = 1-x² and g(x) = x + 3 on the interval [-2,2] 0 2

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Q: 10. Evaluate cos x sin² x dx

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A: Solution:

Q: Joseph completed the two problems, asking him to explain if there is enough information to prove the…

A: Given.