Tutorial Exercise Find the limit, if it exists. lim (8+2) Step 1 Recall from Theorem 3.10 that if r is a positive rational number and c Is any real number, then Ilm x-- Submit Skip (you cannot come back)

Q: drawing the slope field for the differential equation , I would place slope lines of _________ at…

A: We have to find the required

Q: Find the exact value of the expressic ܪܕܐ -1 sin sin ၁ 5 သ | O 2n O 2n 5 5 Эт O 3n 5 3 5

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Q: Find the slope of the tangent line to the curve - x² – 3xy + 3y³ = at the point (1, − 3). - 91

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Q: Question 2 Find the second derivative of the function f(x) = x² - 3x and choose the correct answer.…

A: To find the second derivative of the given function.

Q: Question 1 Evaluate the integral and choose the correct answer. e ln x fethe 01+e O dx 2 01-e A…

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Q: Show the complete solution. Kindly, include the necessary table of values. 4. Thirty percent of a…

A: Given that, Thirty percent of a radioactive substance disappears in 15 years.

Q: A company that produces cell phones has a cost function of C = 112² - 244x + 12581, where C is the…

A: The cost function is given as: C=11x2-244x+12851   We know that, at the minimum value, the…

Q: Bottom of the page is cut off i cannot see the solution.

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Q: (ew - 3) dw? O-ew + C O ew - 3w+C OeW-3w+C O eW-3+C

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Q: the power series ∞ (7-2x)" Consider f(x) = Σ function. 6n n=1 as a a. Find the interval of…

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Q: 9) Erin goes for her daily run. The elevation changes, so she can run some sections faster than…

A: Given

Q: (8) A SUPPOSE VECTOR FIELD FY₁Z) =<X₁Y+Z₁ HAS PARAMETERIZATION z(t)=7+4 AND A x) = ²x WHERE CURUE C…

A: A detailed solution is given in steps 2 and 3.

Q: 1 8. The equation of the image when the line y = x + 1 is translated through (3,-1) is? 1 a. y = x +…

A: Please see the below picture for detailed solution.

Q: Sketch the region R whose area is given by the iterated integral below. Then change the order of…

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Q: Consider the function f(x) this interval. 1 on the interval [5, 11]. Find the average or mean slope…

A: Given, f(x)=1/x

Q: Find the curl of the vector field F(x, y, z)= e sin yi - e cos yj.

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Q: Solve the following initial value problems: A. y(0) = -3: y= B. y(0) - 6: y= dy dt 2t

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Q: Consider the function f(x) = 2x² + 4x - 7. f(x) has a critical point at x = A. Find the value of A:…

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Q: Consider the function f(x) = 3 - 3x² on the interval [-3, 6]. Find the average or mean slope of the…

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Q: Evaluate the definite integral and choose the correct answer. dx 1+5x 0 1 O -In 11+ 5xl + C 5 1 1+5r…

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Q: Let f(x) = x²-1 (a) Make tables of the values of f at values of x that approach x= -1 from above and…

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Q: Evaluate the interated integral: LS-² x² sin(y) dy dx

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Q: Centerville is the headquarters of Greedy Cablevision Inc. The cable company is about to expand…

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Q: 2π 12171710727 17/1xsin nx dx 2π I need to solve the integration in a table or zero method, a…

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Q: Find the derivative of the function g(x) g'(x) = ex + 3xe (2+3x)² = x| X et 2 + 3x

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Q: Find the limit. Use l'Hospital's Rule if appropriate. Use INF to represent positive infinity, NINF…

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Q: Let C be the boundary of the portion of the plane x+y+z=2 that lies in the first octant, oriented…

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Q: 6 A small resort is situated on an island off a part of the coast of Mexico that has a perfectly…

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Q: ¹) (x²y³ + 6xy³) dy + (xy² + 3y²) dx + (x+3) dx = 12y³ dy ; y(²) = 0

A: I have tried all cases to find Integrating factors. According to me last one matches the best .

Q: The sequence is defined recursively. Write the first four terms. a1 = 1 and an = an-1 - 3 for n ≥ 2

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A: To find dy and to evaluate when x=-5 and dx=0.4 for the function y=2x4-45x+1.

Q: A manufacturer wants to design a rectangular box with a square base and an open top. (In other…

A: Let  side of square = x  height of box = y    surface area = area of base + 4 * area of side face…

Q: If the series un is convergent, n=1 then the series (−1)ª un is also convergent. n=1

A: Given first statement is true and second statement is false.

Q: the answer

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Q: If f(x) = 2ln(8 + x), f'(x) = f'(3) =

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Q: 1 tan 4. Express f(x) = t (Hint: Use Integration I as a power series and find its radius of…

A: Please see the below picture for detailed solution.

Q: Show that the average value of sin^2t over [0,2pi] is equal to 1/2. Without further calculation…

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Q: Evaluate O O In 9 3 2 - In 2 In 2 x² 2 O tan¹ (2) tan¹(1) O ln 2 0 1 3 9 dx. x³ + 1 -

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Q: Example 1 Find dy/dx, if a. y=sin(x² + 3x + 1) b. y = cos² (2x-1)

A: I have stated the used formulas in the solution

Q: Let P be the point in R^3 with rectangular coordinates (√2, −√2, 2√3). How to find the cylindrical…

A: We have given rectangular coordinates  (x,y,z) = (√2, -√2, 2√3)

Q: 12. g = ²+1 - 4 2

A: The given problem is solved below in detail.

Q: Find the Cartesian equation for the curve represented by the polar equation, r = 2 sin 0. O x² + y²…

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Q: In Prob. 1-38. Find dy/dx.

A: Given; y=e2x+3.

Q: Consider the function f(x) = 12x5 + 45x¹ - 200x³ + 6. f(x) has inflection points at (reading from…

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Q: 10. A tank originally contains 380 litres of brine holding 450 N of dissolved salt. Eight litres/min…

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

Q: Sketch the region of integration and evaluate the integral: Hint: sin²(z) = (1 - cos(2x)) esin(x)…

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Q: Find the slope of the tangent line to the curve 3 - 2x² + xy + y² I at the point (4, 1). - 27

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

Q: Alden works in the city and lives in the suburbs with Nikka. Every afternoon, Alden gets on a train…

A: We need to determine the time Alden walks.

Q: and f(a) f(x) = 4x² + 5x² + 6x-7 3 7 2. Find f(x), f"(0), given

A: Given a function f(x)=4x3+5x2+6x-7 We have to the following of the given function, f''(x) f''(0)…

Q: Question Find the average value of f(x) = 5 cot (x) csc (x) - 2 over the interval [] Submit an exact…

A: As we know that; The expression for the average value of the function over the interval a,b is:…