SV25-x² In dx , if we let u=/25 - x2 , then udu= - xdx. (A) True B False

Q: Evaluate the following sum of iterated double integrals: r4-2y eAr-r² dx dy 2 2y dx dy +

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Q: 3). 5 dx =

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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: Given the function f(x, y) = {ln (x2 + 4y2 − 4)} / [x + 1] Express the domain of f as a set…

A: The given function,      fx,y=lnx2+4y2-4x+1

Q: Find the derivatives of the given functions. a. y = [ Arc sec(tan x)|· e »<2x

A: use logarithmic function to evaluate the derivative.

Q: | #(9 – In² x)5/2 dx I. Evaluate the following integrals. 1 1. -d.x x(9 – In? x)5/2

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Q: e20 -do 1+ 3e20

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Q: (-1)" (2n+1)! Given: sin x = En=0 x2n+1 for x e R 100 What is the exact value of the sum 2n=0…

A: The series given is: sin x=∑n=0∞(-1)nx2n+1(2n+1)!, x∈ℝ...(1) To find the exact value of the series…

Q: Evaluate the integral. (Use C for the constant of integration.) cos a da sin a

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Q: 7. Find the area of the region that lies inside the curve r = 3cos0 and outside r = 1+ cos0. Show…

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Q: Using Lagrange multipliers, find three positive numbers whose sum is 9 and such that the sum of…

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Q: Evaluate the indefinite integral. (Use C for the constant of integration.) x + 45 dx

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Q: y = (cos COS T 4x5

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Q: Find the original function f(x) from given equation f'''(x)

A: We can solve this as follows:

Q: Consider the following Maclaurin series: (-1)"x²n (2n)! cos x = for all x E R. n=0 1. Let f(x) =…

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Q: Using exact differential equation, determine the solution of

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Q: sin (t) -dt 3 (4+ cos (t))?

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Q: Is it true that if a, < b, for all nE N and E-1 a, is divergent, then E-1 bn is divergent? If false…

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Q: y = [Arcsec(tan r)]ecsc 2r SC

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Q: If f (x) = |x-1| then lim f(x), lim f(x) and lim f(x) are... respectively x-1 x→1- x→1+ x→1 |x-1|…

A: Let's find.

Q: 570 8. The demand function of an electronics company's car stereo is p(x) Find the 2х +7 consumer…

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Q: xsin(x³) dxdy

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

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Q: n(x – 2)" 3" (2n – 1)3 - Consider the power series n=1 a. Show that the power series converges when…

A: We have to check the given series is convergent for x=5

Q: Let graph (x) as below: -6 Solution of lim f(x)is.... x→0* O -2 O 3 O -3 O 2

A: Consider the graph of f(x)

Q: 8. [sin? x cos' x dx Ssin*

A: (8). Given: I=∫sin2xcos5xdx   As we know from the trigonometric identity; sin2x+cos2x=1 And The…

Q: Q2) Solve the D.E xdy + (2y – x* + 3x)dx = 0

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Q: Evaluate the integral ſ xe²" dx; * dx; u=x, dv= e²ª dx using integration by parts with the indicated…

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Q: Function f(x)=x°-6x+1 , increasing on interval .. (-00, -V3) and (V3, 0) 1. O (-v2, vz) 2. O (-0,…

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Q: Find the volume of the solid obtained by rotating the region bounded by the curve y= x+1, y= 0, x=…

A: Let's find.

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: I. Evaluate the following integrals. 1. / 20- dx 2 x)5/2" x(9 – In².

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Q: tan-'(m) m² + 1 m=1 Does the series satisfy all conditions in order undergo integral test? Prove…

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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: -+inf In(tan¯1x) 1+x2 1

A: ∫1∞ln(arctan(x)1+x2dxSubstiute u=arctan(x)→dudx=11+x2→dx=(x2+1)du=∫ln(u)duIntegrate by parts…

Q: vhether the following series is convergent or diverger (-1)"3n² 4n²–1 (b) n=1

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Q: Find Duf at P. f (x, y) = 3(4 +xy)2; P(4,3); u = 1 i+ j NOTE: Enter the exact answer. Duf

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Q: { II. Consider the sequence í n+ 2)! J n=1 a.) Show that the given sequence is monotone. b.) Use the…

A: Here, the given sequence is: πn(n+2)!n=1∞ Let, an=πn(n+2)!

Q: Express the integrand as a rational function and then evaluate the integral. x - 4 dx Jo x² – 5x + 6

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Q: 1. Y = 2 – 7.x fa) — 4 — 5х — 21? 2. 3. Y = 2x³ – 3.x

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Q: 22n (2r 1)". Vn2 +1 nsider the power series n=1 1. Use alternating series test to show that the…

A: Given series ∑n=1∞  22nn2+13  (2x-1)n

Q: Find the area ef"l fhe Shaded reghon a/2

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

Q: ind the sum of the convergent series. +00 3n+1 Z 6n-1 n=0

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Q: . Find the sum of the following convergent series. Σ 00 3n+1 a. 6n-1 n=0

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Q: The round off errors when measuring the distance that a long jumper has jumped is uniformly…

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Q: I 3n O The region bounded by y = sin x and x- axis on the interval [-

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Q: The value of dy/dx for implicit function xy – x + y - 2 = 0 at point x = 1 is ... Nilai dy/dx untuk…

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Q: [ 3x3-2х2-4х-3 х2 (х2+x+1)

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Q: f(x) = -x^2 + x + 20 and g(x) = x^2 - 5x . Compute the area of the region enclosed  by the graphs of…

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Q: 3 < x < 2/3 < x < 3/2

A: We have to choose the correct option from the given options according to the given information