Find the average value fave of the function f on the given interval. e¹/z z² 2 f(z) = [3, 5]

Q: If 8000 dollars is invested in a bank account at an interest rate of 10 per cent per year,…

A: If 8000 dollars is invested in a bank account at an interest rate of 10 per cent per year,…

Q: Determine the derivative with respect to x of: 37+1 b) f(x)=e³ c) f(x)=e* d) f(x)=sin(3x)

A: To determine the derivative with  respect to x of each of the  following functions. (b) fx=e3x2+1…

Q: The owner of a skating rink rents the rink for parties at $440 if 20 or fewer skaters attend. For…

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Q: 5 430 X 32°

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Q: Evaluate the integral. (Use C for the constant of integration.) [7t sin 7t sin²(t) dt

A: Explanation:-

Q: In three-space, find the intersection point of the two lines: [x, y, z] = [-2, 3, −3] + t[1, x = 3-t…

A: We have given that Two lines  [x, y, z] =[-2,3,-3]+t[1,-1, 2]  ----(1) and   x=3-t y=-5+ 2t…

Q: The function y = Ce-2 +3 Solves the differential equation y' + 3y = -2y + 6. O true false

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Q: Given f(x)= ((n+1)(n+2)(n+3)....(n+2023))^(1/2023) then find lim n approaches to infinity f(x)(means…

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Q: Evaluate sin (‡) dxdy- -π/2 cy² 1

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Q: Find the area enclosed by the ellipse a² b + y=-b√√√a²-x² y² 62 b y=1/√√a²-x² = 1 shown in the…

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Q: Provide an appropriate response. If cos x is replaced by 1-- O JE] < 0.000014222 OE < 0.000085333 O…

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Q: O Make a graphical tool to approximate the limit of the function. If necessary, round to three…

A: The limit of a function can be found by using the graph or by finding the table of values to the…

Q: Find the first three terms of the Taylor series in x - a. ex. a=3

A: Given that a function f(x) = ex and a=3. We find first three terms of taylor series.

Q: - y=t? –t, t = 2x2+1, what's the dy dx for x=1?

A: We know that the derivative of x^n=nx^(n-1)

Q: The owner of a skating rink rents the rink for parties at $700 if 50 or fewer skaters attend. For…

A: The owner of a skating rink rents the rink for parties at $700 if 50 or fewer skaters…

Q: Use integration by parts twice to evaluate fet cos(3t)dt: Step 1: Let u = et and du + S fet…

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Q: Using the the derivative method power rule. How come the answer is 2t^-3? Instead of 2t^1?

A: Given: f=-1t2 We are required to find: The derivative of f

Q: d the indefinite integral using integration by parts with the given choices of u and dv. (Use C for…

A: using  Integral by parts:-  ∫u v dx = u∫v dx −∫u' (∫v dx) dx  here u = ln(x) and v = x^3   u' = 1/x…

Q: Find the local linear approximation of f(a) = 2√ at x = 4. Oy=(x-4) O y-2√x-4 Oy=4 Oy=x+2

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Q: (ln(t))4 dt t

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Q: Sx.cos5(x²)dx

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Q: Making this substitution using [₁ gives us 10 sin²(x) cos³(x) dx 10 10 sin²(x) (1 - sin²(x)) cos(x)…

A: To evaluate the following integral. ∫10 sin2x cos3x dx Note: After seeing the previous solution, we…

Q: Given cos(x): 11/123 on the interval [0, 2π], what is the value of x?

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Q: Question 12 O O Which of the following is equivalent to C ? 10 6 10 C 10 16 C 10 10 C 4

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Q: Find the partial derivatives gæ, gy and 9% for the function g(x, y, z) = xy + x² z − yz³

A: Given :- The function gx,y,z=xy+x2z-yz3 To find :- The Partial derivatives

Q: Estimate S M₁~ e -x2 dx using the Midpoint Rule with n = = 4, correct to 5 decimal places.

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Q: Divide. 4+i -2+3i Enter your answer, in standard form for complex numbers, in the box. 4+i -2+3i ||

A: Given

Q: 1. In three-space, find the intersection point of two lines ₁ = (–1,1,3) + t(1,2, −2) and r₂ =…

A: The given two lines are: r1→=(-1, 1, 3)+t(1, 2, -2)Andr2→=(5, 3, -3)+s(-2, 1, 1) where s, t∈ℝ

Q: Question 10 Given m = 6, n = 1, and v = (-4, 7), what is v(n-m)?

A: The given values are: m=6        and        n=1v=-4, 7

Q: Find the value of d2y/dx2 at the point defined by the given value of t. x-9 sin t. y - 9 cost, t =…

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Q: 33. f(x) = X 2 x2 - 1

A: As per guidelines we support only three subparts of the questions.kindly repost next questions

Q: 6. y cos5 (sin(2x)), y'=?

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Q: Find an equation of the plane passing through the three points given P = (4, 2, 9), Q = (6, 7, 18),…

A: We have given three points as P = (4,2,9) Q = (6,7,18) R = (11,8,12)

Q: What is an antiderivative of the function x + 2xln(x)? x²ln(x)+2023 xln(x) +2023 In(x) + x xsin(x) +…

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Q: Use integration by parts to establish the reduction formula: [(In x)" daz = 2(lnx)" - n [ (in…

A: ∫lnxndx Integration by parts ∫udv=uv-∫vdu

Q: What is the complex number z = -3 + 3√3i represented in polar form? Enter your answer by filling in…

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Q: For each of the following infinite series, determine whether the series is absolutely convergent,…

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Q: ate the me tegral, √ xy² xy² ds, C is the right half of the circle x² + y² = 4 oriented…

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Q: thank you for the explanation but i think you misunderstood me the exam is an mcq exam of 25 minutes…

A: Given integral,I=∫011(x-2)x2+2xdxWe need to find whether the given integral converges or diverges…

Q: Find the Taylor series at x = 0 for the function by calculating three derivatives and using the…

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Q: Prove Or disprove the the following: d dx a (xarctan - in (a² + x²)) = arctant a

A: ddxxarctanxa-a2lna2+x2=arctanxa

Q: 2 F5V/² W

A: let f(w)=5w25

Q: Match each of the following vectors with its magnitude. t = (-7, 1) u = -2i-8j a vector with an…

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Q: Part 1 Find the binomial coefficient. 7C5 20C15   Part 2 (Use the binomial theorem to expand…

A: Binomial Theorem: a+bn=C0nan+C1nan-1b+C2nan-2b2+C3nan-3b3+......+Cnnbn. Binomial coefficient:…

Q: Find the area of the surface generated by revolving the curves about the x = sin t, y = 1 + cos t, 0…

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Q: Does the series converge or diverge? Please justify your answer in detail, mention any tests you…

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Q: Determine the following limit: 2e 2x Him (2²-2-2) x-0

A: limx→02ex-2x-25x2

Q: Graph the function and find the limit (if it exists) when x approaches 2. [2x + 1, x < 2 x + 3, x ≥…

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Q: (b) Use the function to find T(30,000). $ (c) Find the tax due on a taxable income of $120,000.

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Q: 1. The function is given piecewise: ƒ(x) = cos(x) 0 X if x 0

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