= Use the limit definition of the derivative to find the slope of the tangent line to the curve f(x) x = 3. 3x² at

Q: Find the volume of the solid generated when the region ? bounded by the given curves is revolved…

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Q: 2. Verify using the principle of Superposition that y₁ = ²* and y₂ = e* are solutions of y" - 7y'…

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Q: Using trigonometric substitution, A) None Ⓡ/ B Ⓒ D sec58d0 tan²0 tan40d0 sece * sinᎾdᎾ cosA Ss x4dx…

A: ∫x4(1+x2)32dxPerform trignometric substitutionSubstitute x=tan(θ)→θ=arctan(x)→dx=sec2θ dθ

Q: Find the derivative of f(x) = ✔ (6x¹ + x² − 1) 5.

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Q: 3 [(V) dt -

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Q: Evaluate the double integral that will find the volume of a solid bounded by z = 4 − x^2 − 4y^2 and…

A: Let's find volume of solid.

Q: Find the volume of the solid generated by the region bounded by -x + y² = 8, x = -2y and y = -2…

A: We first sketch the region using a graphing calculator:   We can find the y-coordinates of the…

Q: i can't understand your solution

A: We have to explain the solution.

Q: 3x + 2y = 6; x = 0; y = 0; axis OY. Find the moment of inertia.

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Q: If fx √1- x4 dx = ge ½ A B 0 C D) 1 H|2 H|4 g(e) de, then 9

A: We can solve the given integral by using substitution.

Q: 2. If the first term of an arithmetic sequence is 3 and the common difference is 4, what is the 23rd…

A: Topic = Sequence

Q: A ball is thrown upward from the top of an 800 foot tower. It's height above ground, h, t seconds…

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Q: In the quadratic equation Ax²+BX+C =0 The roots are real and distinct. The roots are complex…

A: The given quadratic equation is Ax2+Bx+C=0

Q: II. Consider the polar curves C₁ : r = 3 (in blue) and C₂:r = 2-2 sin (in red) and let R be the…

A: Given that polar curves  C1 : r = 3  and C2 : r=2-2sinθ  we have to find all points of intersection…

Q: Find the moment with respect to the y-axis of the area bounded by the parabola x = 9y - y² and y =…

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Q: Find the acute angle between two tangent lines at point of intersection between two curves xy = 5…

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Q: Solve for the variable using a method of your choice. 72+7+72+6 7x+6= 8

A: The detailed solution is given below Thank you

Q: Find the area bounded by the parabolas (x - 1)² = 4ay and y² + 4a = 4ax.

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Q: he variable in each equation using a method of your choice. 93x+4 = 27-x+6

A: Given problem:- The variable in each equation using a method of your choice.   93x+4 = 27-x+6

Q: c) 3,-1, -3, 3, -9, -27, ...

A: If the difference between two successive terms of a sequence is constant, then the sequence is…

Q: Evaluate the following integrals. -1 L₁ (3²- (3x² - 4x−¹+2) dx

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Q: Find the area bounded by the curves x² + y = 6, y = x, y = -2 and x = -2.

A: I have shaded the area green which is to be calculated

Q: TYPEWRITTEN

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Q: 0 W³ 6w² +3 dw

A: Given, ∫01w36w4+3dw

Q: 3) Use L'Hopital's Rule to evaluate and check your answers numerically: sin x (a) lim X x→0+

A: Solution: a) limx→0+sin xx1x2

Q: Use the slopes of tangents to determine whether the function -6x2+36x is increasing, decreasing, is…

A: Given function, f(x)=-6x2+36x We know that function is said to be increasing when f'(x)>0, and…

Q: f(x)=8x¹-7x³+2 on [−2,1]

A: To compute the average value of the given function f(x)=8x4-7x3+2 on [-2, 1]

Q: Let f(x) = log2 (4x-x²)+2x. At what point is the tangent to the curve y = f(x) perpendicular to the…

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Q: What is the inverse for the function f(x) = 2+3/1-x? A. f1(x)=1-(x-2)³ 1 B. f¯¹(x) = 2+³/1-x C.…

A: Given that:  f(x)= 2+ (1-x)1/3 and we find the value of f-1(x).   Here i attached the solution of…

Q: Find the derivative of the following functions. Use long method. a. f(x) = 3x² + 5x - 100 b. f(x) =…

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Q: Let C, D and E be the polar curies below: Cir=f(0) = 3-3 Cos 0 Er = g(0) = 12/250c4 D:r=3 (1.) Show…

A: Let's solve part 3 and 4.

Q: 6. f(In x)² dx

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Q: -1 valuate the following expression without using calculator : tan sin (³²) +cos 35 - 12

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Q: 2- Compute 1+i 2-51

A: Given that,      1+i2-5i

Q: y = (1+x)² 2 x² 2

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Q: 1. Consider the function f(x) = x6 - x³. a. Determine the absolute extremum using the First…

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Q: 5. Calculate the sum of the first 23 terms of the sequence defined below. tn 10+ 3n, n E N

A: We have to find the sum

Q: f f(x) = 3 - 2x and g(x) = ln (x - 1) then (image attached) = 1. -2 2. None of these 3. 3 4. 1

A: Here, f(x)=3-2x, g(x)=ln (x-1) Now,…

Q: If a sphere passes through the points A(0, 1, 2) and B(−1, 2, 2) and its center C lies on the…

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Q: Consider vector v = (1,2,2), point A(2,5,4) and point B(-1,5,1) - In center-radius form, find an…

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Q: Find the area bounded by the curves x² + y = 6, y = x, y = -2 and x = -2.

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Q: x3-4x-10 x²-x-6 dx.

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Q: Solve • ƒ²₂(x + 1)(x + 2)²(x² - 1)dx with and without the even-odd theorems (show both solutions).

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Q: 2x fe²x sinx dx

A: Using integration by part.

Q: Solve the following trigonometric equation for 0 ≤ 0 < 2π. Show your work. 4 cos²x 3 =

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Q: 1. A certain ellipse is centered at the origin from which the major axis is always equal to 25 and…

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Q: Determine the Cartesian equation of the tangent line to C1 at the point where 0 = π/2. Given: polar…

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Q: Let C be the parametric curve defined by Ja(t)=1²-t-6, [y(t) = 41³ + 3t² - 6t. Determine the point/s…

A: a) Given that: xt=t2-t-6yt=4t3+3t2-6t For a horizontal tangent line, the slope must be 0. That…

Q: 4. Determine the number of terms in the sequence: -45, -32, -19, -6, 410 ***

A: There are 36 terms  in the sequence.

Q: 23. Test the series below for convergence using the Ratio Test. Σ n2²n 8n-1 n=1 The limit of the…

A: Here we have, ∑n=1∞n22n8n-1