8 lim x-2+ x²-4 x→2+ X x-21

Q: lim (t i − 4 j + t² k) 1-9 ■im (t i − 4 j + t² k) = i →9 i+ i

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Q: he equation of the line that passes through the point (-4,-2) and is parallel to the line y=4x-8 is…

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Q: Determine whether the improper integral diverges or converges. 6° x²ex dx converges O diverges…

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Q: 11. Given the function below, what is its derivative? * f(x) = 2x - √x f'(x) = 2x C f'(x) = 2 - a 1…

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Q: Find d² y dx² for x³ + y³ = 2 43

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Q: Solve for the limit of the following limits functions. Write your answers in simplest forms. If the…

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Q: 2. Find a power series solution of the differential equation y' = 4y

A: To find a power series solution of the following differential equation.y'=4y

Q: 55. the sum of the first 80 positive integers 56. the sum of the first 120 positive integers

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Q: Consider a triangle ABC like the one below. Suppose that C= 123°, a= 15, and b=37. (The figure is…

A: The Cosine rule; a2=b2+c2-2bccosAb2=a2+c2-2accosBc2=b2+a2-2abcosC Given: C=123°, a=15, b=37

Q: Determine whether an exponential function, a logarithmic function, or a linear function is the best…

A: Given the query is to find the best fit function.

Q: [18x² √6x³ +5 dx 3 ○a. — (6׳ +5)³/4 + C b. (6x³ +54/5 + Oc.5(6x³+5)¹/5 + C d. 5 Od (6x³+5) ³/4 + C…

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Q: D Question 5 Find the derivative of -2x f(x) = x f'(x) = -2x²e-2x (E) None of these f'(x) = e-2x…

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Q: Determine if y=5 cos x and x=31²-5t+3 dx

A: Given,             y=5cosx , x=3t2-5t+3To find : Determine dydt

Q: Calculate d^2 f where f(x,y)=e^x sin⁡y.

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Q: Find the length and width of a rectangle that has the given area and a minimum perimeter. Area: 7A…

A: Area of the Rectangle =(Length)(width). Perimeter of the Rectangle=2(length+width).

Q: Consider à = (2,1,k), and b = (k,-8,k). Find the value of k such that å and bare perpendicular.

A: We can find the values of k as below.

Q: In (x² + y² ) = 2 arctan y' 9 X

A: We know that derivative of xn is nxn-1.     Here i attached the solution of this question.

Q: Evaluate the following integrals. Show complete solution and your answer must be in simplified form.…

A: To Find :   ∫11+cosxdx

Q: L=

A: Follow the procedure given below.

Q: Use an appropriate linear approximation to estimate cos(60.5°). (Round your answer to three decimal…

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Q: Evaluate the iterated integral. LS²(x+y (x + y²) dx dy

A: Given query is to find the value of the integral.

Q: . find f'(x) if f(x) equals the given expression. a. log (x4 + 3x2 + 1) b. log (3x2 + 2)5

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Q: Define a weakly quasi-concave on a Cobb-Douglas Function

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Q: f(x) = t^2(t - 7)^1/3.   Find all critiacal points and all relative maxima

A: Solution is given below:

Q: the

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Q: Find the area of the triangle below. Carry your intermediate computations to at least four decimal…

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Q: 1. What rule is applied in the following given? * Dx (-13) = 0 Power Rule of Differentiation Product…

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Q: Question 8 Find the derivative -[f (x)] dx Anmospace support = 3 In (In (x²-3x + 5)²) 3(2x - 3)…

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Q: 4. Use cylindrical coordinates to evaluate [!] √²³² + y²dv₁ D where D is the region that lies inside…

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Q: Find an equation in rectangular coordinates for the surface represented by the spherical equation. 프…

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Q: Given that the tangent and normal to a curve at point P(x, y) meet the x-axis in A and B…

A: It meets the x axis in A and B respectively and y axis in D and E respectively.To Find: Family of…

Q: This is the length of the major axis, not the minor axis.

A: Apologies for the inconvenience.   Given equation is: 7x2+y2=49 We write it in the form: x2a2+y2b2=1…

Q: c. y = 4e (3x²-x) C.

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Q: Find the derivative of f(x) = tan(sin(2x))

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Q: Current Attempt in Progress Find the exact arc length of the curve .x = 1 = = √ ( ₁² + 2) ²/² ₁ +…

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Q: 1 (s² + a²) (s² + b²) a sin at + b sin bt a² - b² b sin at a sin br - ab (b²-a²) cos at + cos bt…

A: This question can be solved using the concept of inverse Laplace transform.

Q: 1. A man on a wharf, whose hand is 8.2 m above the level of the water surface is pulling a rope tied…

A: Given;  Rope length =20m Height =8.2m

Q: Find the derivative of y= (2x³+x+1) 4(x²+3)5 (x4+3) 3 O A dy (4) (2x³+x+1) ³ (5) (x²+3) 4 dx 2(x²+3)…

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Q: Use any method to find the Area of domain bounded by curve parametrized by X = cos³t₁ Y = sin³t, 0≤…

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Q: Describe the graph of the equation. r = 5 cos ti - 8 sin tj+ k O An ellipse in the plane z = 1,…

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Q: Find the present value of a $30, 000 annual income stream if it is invested immediately as it is…

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Q: Question 5 > The plot below represents the function f(x): 3 3-4-32 1 2 3 4 Evaluate f(-3): f(-3) -…

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Q: owin - y" −4y' +4y=0 L".

A: 1)  y''-4y'+4y=0 Auxillary equation is m2-4m+4=0m2-2m-2m+4=0m(m-2)-2(m-2)=0(m-2)2=0 ⇒m=2,2

Q: 9x²-6 2x²-x²-8x+4 B D + x + 2 mx + n None of the choices 4 To evaluate A x-2 A 9 B 3 E 2 S + -dx…

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Q: \1/2 2. y = (2 tan² 20-1)

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Q: An experienced carpenter can frame a house twice as fast as an apprentice. Working together, it…

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Q: B) Estimate the next root of the function f(x)=x^3-x-1 using Muller method, let x0=1, x1=2, x2=1.5

A: Muller method: The Muller approach is applicable to any root-finding programme, but it is especially…

Q: Find the Taylor series of the function at the given center a. f(x)=x³-5x, a=2

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Q: 3. Let h = f(t) be your height (in meters) above the ground while riding a Ferris wheel. The Ferris…

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Q: [10 sin(2x) cos(2x) √ cos²(2x)-5 dx O a. 5 (cos² (2x)-5) ³/5 + C 3 5 O b. -(cos² (2x)-5)³/2 + C OC.…

A: To evaluate the given integral.