Choose one(1) from the following question to be answer. The graph of each rule must reflect on your solution paper. A. Approximate the area under the f(x)=2x² + 12 from -2 to 7 using 9 intervals B. Approximate the area under the f(x) = sin(x + 1), [-2, 4], n = 6 C. Approximate the area under the f(x) = -x³ + 3x²-2, [0, 2], n = 4

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Q: Find Vf at the given point. f(x,y,z) = x² + y² - 3z² + z lnx, (1,2,3) Vf|(1,2,3)+( = )j + (k…

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Q: Find the length of the curve y = ln sin x from t = −2 to t = 0.

A: f(x)=y=ln(sinx) Arc length =∫ab1+(f'(x))2dx f'(x)=dln(sinx)dx=1sinxdsinxdx=cosxsinx=cotx a=-2 b=0

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Q: If xs2 + yt2 = 1 and x2s + y2t = xy − 4, find ∂x/∂s, ∂x/∂t, ∂y/∂s, ∂y/∂t, at (x, y, s, t) = (1, −3,…

A: We have to find the values of partial derivatives.

Q: -3√3 dx √3 x² √√x²+9 2

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Q: 4. Evaluate the following limits. a. lim X→→→+** 2x 3x² b. lim c. lim -3/x X In5 x x²

A: This is a problem related to limit calculation. Based on the general formula and concepts we will…

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A: We have to draw the diagram and time required.

Q: əz Let z = x² + y³, x = 2st and y = s-t². Compute for and ar

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Q: M8 1 Σ n=1 h n’ + 8 +8 3

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Q: whose equation is y³ + 2xy + x² = 9 Using techniques we have learned in our course, perform the…

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

Q: (1, -2) (a) The curve with equation y2 = x³ + 3x² is called the Tschirnhausen cubic. Find an…

A: We have to find the tangent equation and draw the graph.

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Q: Find the critical points and sketch the graph of the function. 1. f(x) = √5 + x 2. f(x)=x²-3x³ + 3x²…

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Q: Determine el valor de a € tal que: 80 ex e2x + 1 58⁰ a -dx = R+

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Q: 5. Find the limit using any method of choice. x + 2 lim x-2 2x² x 10

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Q: f I. Evaluate tan 2x dx

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Q: 9) Find the equation of the tangent to the curve y = 1+ Int and x=t+Int when t = 2.

A: Given problem:- Find the equation of the tangent to the curve y = 1 + lnt and x=t+Int when t = 2 .

Q: Give the tightest possible bound (as a Big-O of N) for each of the following functions: 1) f(N) =…

A: Given

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Q: Solve the system of differential equations. x₁' = 3x1 - 1x₂ ¸x₂' = 1x₁ + 5x2 x₁ (0) = - 11, x₂(0) =…

A: This is a problem related to solving system of linear differential equation. Based on the general…

Q: 5x=2 5. Find the member of the curve whose slope at any point is y+s point (3, 2) and passes through…

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Q: Evaluate the integral: fe* sinhxdx. Select one: O a. -+C 0b. ²+0 ++ C d+C

A: We can solve this as follows:

Q: Physical Applications of First-Order Differential Equations A body at a temperature of 50° F is…

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Q: Evaluate the following integrals: (show solution) a x² +2 b.) 1 x+1 x+√x c) f(sec x d.) e 4x 4x+1 x…

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Q: A plane that passes through the points A(2,1,1) B(-1,-1,10) C(1.3.-4). Find a vector perpendicular…

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Q: RIN Find the linearization L(x,y) of the function f(x,y)=e4x cos (3y) at the points (0,0) and 0₁-…

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Q: clnx Find the integral of ²x ye²dzdxdy

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Q: Find the derivative of the function y = (4x + 1)4(5x + 1)-5. dy (16x+4) 3 (4x+1)4 dx (5x+1)5…

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Q: 1) Find the radius of convergence and interval of convergence of the series. Show All Your Work.…

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Q: Evaluate the following limits 2x a. limx→>+00 3x²

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Q: An open-top rectangular box is being constructed to hold a volume of 400 in ³. The base of the box…

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Q: Determine the indefinite integral. 25 dx x In 7x 25 S= Sx157x x In 7x dx =

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Q: Find critical points of ƒ(x) = x² ln(x) — 1⁄x² on the interval (0, ∞).

A: Given; fx=x2lnx-12x2 ; x∈0,∞    As we know that; The critical points of the function, y=fx can be…

Q: 3. f(x)= x² + 3

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Q: Find the length of the are of the function x² = 4y from x = -3 to x = 3.

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Q: Using the laplace transformation table, evaluate the following, considering any other variable other…

A: Ths question can be solved using the formulas of Laplace transform.

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Q: This question is designed to be answered with a calculator. A kettle of hot water, initially at…

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Q: Determine whether the following statements are True or False? y = f(x) 2 X (a) lim f(x) = 1 (b) lim…

A: Diagram is given. Determine whether the following statements are true or false

Q: Without using the graph, determine all inflection points of a + x².

A: For inflection point , set f''(x)=0.

Q: Evaluate the given integral Q. Q = ff (√5 - x) dA, R where R is the region bounded by y = x and x =…

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Q: Sketch the region of integration of the given integral Q in No. 1. Set up Q by reversing its order…

A: We need to set up integral.

Q: Sx" xn sinx dx = −x” cosx+n n-1 cos x dx

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Q: 2 2 dx 2x (V2x + 9)

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Q: 2. Which is the interpretation of the statement lim f(x) = L? i. For all x values close to c, but…

A: As per bartleby guidelines we only give first three question answers.

Q: Solve the following problems showing detailed solutions.Draw the complete figures for each question.…

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Q: A product is introduced to the market. The weekly profit (in dollars) of that product decays…

A: First we rewrite the profit function in terms of t.Then differentiate p(t) with respect to t.

Q: If zs² + yt²= 1 and 2²s+y³t = ry - 4, find 0x/0s, az/at, Əy/08, Əy/ot, at (x, y, s. t) = (1, -3,2,…

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