Find the value of 7x²e-3 Determine whether ) (7n’e- ) n=1 Enter C if series is convergent, D if series is divergent.

Q: To input your angle measures in degrees, use the functions sind (5), cosd (5) and tand (5), instead…

A: This is a problem of a trigonometry. Based on application of trigonometry. Please follow the below…

Q: x² + 2 (х - 2)(х2 — dx 2x + 2) **

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Q: Q2) Solve the D.E xdy + (2y-x* + 3x)dx D %3D

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Q: Find the sum of the following convergent series: [tan(2n – 1) – tan-(2n + 3)]. n=0

A: Here, the given series is: ∑n=0∞tan-1(2n-1)-tan-1(2n+3) which is a telescoping series. Let,…

Q: 1. Identify the type of conic section whose equation is given, then find the vertices and foci. Show…

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Q: Determine whether the planes are parallel, perpendicular, or neither. Зх — 18у — 15г - 2 %3D 0 (a)…

A: Given:   Equations is given

Q: 3. Give the parametric and symmetric equations of the line that passes through the point (4, -3, 5)…

A: topic - equation of a line

Q: state whether Converges diverges

A: To state whether the given series converges/diverges. ∑n=1+∞-1nnnsinn1n2n

Q: 4). | (5 sin 2x) dx = 2

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Q: Evaluate the following integrals. 1 dx (e2r – 4)³/2

A: The integration of the integral is 1/(e2x-4)5/2.

Q: sin r cos r dr

A: We have to calculate the given integral

Q: d²y Find and dx then simplify whenever possible. dx2 1) y = 3t5 – 2t x = 4t3 2) y = t-3 – 7 x = t2 –…

A: We have to find first and second derivative for the given parametric function.

Q: 1 1. d.x J #(9 – In² æ)5/2°

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Q: Evaluate the integral. 3 + 2 | du

A: This is a definite integral which can be solved using below formula    ∫ab f(x) dx= [ φ(x) ]ab = φ(…

Q: Find all solutions of cos (z2) = %3D (Leave your answers in exact form and enter them as a…

A: Solution of cos(x)=cos(y) isx=2kπ±y

Q: | 62* cos (2*)

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Q: Show that the equation has exactly one real root. x° + e* = 0 3

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Q: Necessary and sufficient condition for a function y = f(x) to have a maximum value is...…

A: Let's find.

Q: 3/2 5. Find the exact area of the surface obtained by rotating the curve x =- Show All Work and Give…

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Q: Show clear and detailed solutions. Given: Let A = (1,0, 2) and B = (6,–2, 3) Solve and calculate for…

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Q: Q3) Evaluate triple integral SN S dz dx dy . x-y

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Q: let k be a positive real number. Then f(x)= squareroot of k^2-x^2 is continuous on the interval: a)…

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Q: V. Let f(x) be a differentiable function such that for all x > 1, f(x) • f(x) > 1, f'(x) (-1)" f(n)…

A: Solution is given below:

Q: 6z* cos (r*) dr-

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Q: Find the most general antiderivative of the function. (Check your answer by differentiation. Use C…

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Q: An evergreen nursery usually sells a certain shrub after 9 years of growth and shaping. The growth…

A: topic - differential equations

Q: solutions

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Q: Vx² – 4 dx

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Q: A(-4, 4), B(12, 12), and C(16, 0). Medians CD, BF, and AE are drawn. dians of triangle ABC are…

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Q: Preview Activity 1.4.1. Consider the function f(x) = 4x - x². a. Use the limit definition to compute…

A: This question can be solved using the concept of limit definition of derivatives.

Q: 3. Find the exact length of the curve. Show All Work and Give Answer In Simplest Form. x=1+3r²,…

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

Q: 678 COS (x³) dx 3

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Q: Which of the following vectors are linearly independent?

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Q: Find the directional derivative of the function at P in the direction of v. f(x, y, z) = xy + yz +…

A: To find the directional derivative of the function at P in the direction of v.fx, y, z=xy+yz+xz, P1,…

Q: 6. Find the surface area generated by revolving the curve x = 5 cos' t, y = 5 sin' t, 0sts, about…

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Q: Let an = n> 1. In(2" + 1)' 1. Determine if the sequence {an}1 is convergent or divergent. 2.…

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Q: 8x2 – 5 dx (2 — 1)(4г2 + 1) 6х —

A: To sove the following integration by using partial fractions.∫6x-8x2-52x-14x2+1 dx

Q: - Evaluate the following integrals. 1 1. J x(9 – In² x}5/2 dx

A: To evaluate: ∫1x9-ln2x52dx Let, I = ∫1x9-ln2x52dx

Q: dy Find dz and simplify: y = ln(2x + V1 + 2a²)

A: The objective of the question is evaluate the derivative of the given function.

Q: х2 — 6х + 9 dx V6x – x²

A: Given,           ∫x2-6x+96x-x2dx

Q: Question Given that 0 < x < 2n, find all the solutions to the equation 8cos?x = 8cos x + 6. Provide…

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Q: dy Find da and simplify: y = tan(ev)

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Q: Given: a, = In(n + 1) – In(n) for n E N || Determine if the following is convergent or divergent.…

A: Given  an = lnn+1 - lnn for n∈ℕ.

Q: Q4) Find plane area inside the polar function r = 2 and outside the polar function r = sin (-0) +1…

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Q: fundam nob

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Q: x² + 2 xp (х — 2)(x2 — 2х + 2)

A: The given integral is: I=∫x2+2x-2x2-2x+2dx   We know that; ∫1ax+bdx=1alnax+b+C

Q: Plot and label the following polar points (r, 0) in the xy-plane. (a) A= (-1,57/4) (b) В %3D (2,…

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Q: Find the surface area of that part of the plane 9x + 6y + z = 4 that lies inside the elliptic…

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Q: 2. Determine all critical points for the following. Identify the maxima/minima. 2/3 a) y = 6x - 4x +…

A: A critical point is a point in the domain of function where function is either non differentiable or…

Q: Use Part 1 of the Fundamental Theorem of Calculus to find the derivative of the function. tan(x) Vot…

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