3.1. Determine the response y(t) of the differential equation below d²t dt² dy + 2y = 2 where y(0) = y'(0) = 0 dt +2- 2

Q: Question 1. Let f(x) = (x³ + x² + 1)e²³+1 and g(x) = e³+1. (a) Draw a rough sketch of the graphs of…

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Q: Use the tabulated values of f to evaluate the left and right Riemann sums for n=10 over the interval…

A: By using the tabulated values of  to evaluate the left and right Riemann sums for   over the…

Q: Find the exact length of the curve. x = 1 + 9t², y = 3 + 6t³, 0≤t≤3

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Q: Problem 4 Suppose that the utility function is U (x, y)= a lnz+biny, and that we have a standard…

A: Solution is following in step 2.

Q: Use the continuity of the absolute value function ​(x is continuous for all values of​ x) to…

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Q: 4. Find the limit of the sequence an = 2arctann n³ +4

A: The given sequence is

Q: Find f(x) if y = f(x) satisfies dy dx and the y-intercept of the curve y = f(x) is 2. = ƒ(x) = = 104…

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Q: 5. Evaluate fff y dv with E = {(x, y, z): 0 ≤ x ≤ 3, 0≤ y ≤ x, (x−y) ≤ z ≤ (x + y)} E

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Q: Newton's Law of Cooling tells us that the rate of change of the temperature of an object is…

A: By Newton's Cooling Law =Proportionality constant ambient temperature Temperature of an object

Q: 3. For which x value(s) is ƒ(x) = = why. 10+ x x² -9 - 1 2x continuous? Explain

A: f(x)=10+xx2−9−12x

Q: Find 12+15+18+21+...+1056 using a technique from this section.

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Q: Write out all functions ƒ : {1,2} → {a,b,c} (in two-line notation). How many functions are there?…

A: Given function

Q: pean 3 (4) Consider f(x, y) = x²³-12xy + 8y³ Find the critical points and classify them as a local…

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Q: If √√x+√√y = 6 and y(25) = 1, find y'(25) by implicit differentiation.

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Q: y"-2y' +24y=3sin(4x)+6cos (7x)

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Q: explain why the integral test cannot be used to decide if the series converges or diverges. α) Ση…

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Q: show work .

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Q: Find all solutions to the equation. 2 cos 0 + √2=0 Write your answer in radians in terms of , and…

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Q: 2 lim (√√x² + 1 -√√x + 1) X x →∞

A: By using L'Hospital's rule to evaluate the following limit.

Q: Complete the following steps for the given function, interval, and value of n. a. Sketch the graph…

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Q: show all work

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Q: nction y = f(x) looks like this: what y = fl (x) would be ? चि etermine what X लिए फ tr LD

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Q: bounded by the 0 6 Calculate SS x²dA where R is the region R Ellipse 9x² + 4y² = 36. Use a…

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Q: Can we do it without the squeeze theorem?

A: To solve the limit without using squeeze theorem.

Q: Find the extreme values of f(x,y,z) = x² + 2y² + 3z² subject to the constraint x-y-z = 1. 6 O A.…

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Q: Let f(x) = 30 1+ 23-x a. Use tables and graphs to find lim f(x) and_lim_ƒ(x). b. Identify any…

A: As per the company's guidelines, we are supposed to solve the first three sub-parts for you, Kindly…

Q: Using rectangles whose height is given by the value of the function at the midpoint of the…

A: Using the midpoint Riemann sum, we can estimate the area.

Q: Find the volume of the solid graduated by revolving the area bounded by the given curves about the…

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Q: show work.

A: 18)  Graph of the function is shown below

Q: Suppose that a thin metal wire in the shape of a semicircle occupies the curve C, where C is the top…

A: Given the mass density of the wire is

Q: Find the following cardinalities: a. A when A= {5, 6, 7, 8, ..., 34}. b. A when A= {x € Z : −6 ≤ x ≤…

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Q: Find the inverse Laplace transform f(t) = L-¹ {F(s)} of the function F(s) = f(t) = L-¹ 6 s² +9 2s s²…

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Q: A 200 gallon tank initially contains 100 gallons of water with 20 pounds of salt. A salt solution…

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Q: 1. Evaluate each limit: lim x+5 3x x² +1

A: Since you have asked multiple questions in a single request so we will be answering only first…

Q: Question 2. Find the global maximum and global minimum of the function f(x) = x²e² on the ellipse x²…

A: To find: The global maximum and global minimum of the function on the ellipse .

Q: How does one go about solving this? I could use some help please. 4 5 Assume s = 0 corresponds to…

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Q: A: The plane Ax - By + Cz - 1 = 0 pass through non collinear points (1,1,0), (2,0,-1) and (2,9,2).…

A: Given that the plane  passes through non collinear points

Q: 5. What is the instantaneous rate of change at x=2 for the function f(x) = 2x - 5

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Q: 3. Determine the sum of the following series, Σ n=0 Π (n + 1)!

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Q: Find the area bounded by the given curves 1.) xy = 1, y = x, x = 2 and y y = 0

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Q: Consider the function f: N→ N given recursively by f(0) = 1 and ƒ(n + 1) = 2 · ƒ(n). Find ƒ(12).

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Q: Express the following sums using sigma notation. a. 1+3+5+7+...+99 b.8+11+14+...+32 c.…

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Q: Consider the following initial value problem that involves a Bernoulli differential equation: dy 6 +…

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Q: Consider sets A and B with |A| = 12 and |B| = 19. a. How many functions f: A → B are there? b. How…

A: Consider sets A And B which |A|=12,|B|=19.

Q: Use implicit differentiation to find the equation of the tangent line to the curve xy³ + xy = 12 at…

A: Given query is to find the equation of the tangent line.

Q: Using the Law of Sines to solve the all possible triangles if ZA= 117°, a = 29, b = 20. If no answer…

A: Sine law is given as follows As we know that the sum of all the angles of a triangle is

Q: 19. f(x) = ln(2 + x) in powers of x - 2

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Q: Solve the initial value problem: y'= -0.04y + 20 y(0) = 30 y(t) =

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

Q: 18. lim f(x) x→1 f(x) = x² + 3, 2, y 6 2 ++ H -2 + 2 x = 1 1 X = 4

A: Given: The graph of the function  is given below.To Find: By using the graph to find the following…

Q: A circle has a radius of 18ft. Find the lengths of the arc intercepted by a central angle of 1.7…

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