By Maclaurin series expansion, show that the sum of the geometric series may be written as a power series given by a = a aΣrn-¹ = a +ar+ar² + ar³ + ... + ar”−¹ + ... 1-r n=1

Q: e2-1 Evaluate: limx→0 2x²+x 01 O ∞ 00 O None of the choices 02

A: The given limit is: limx→0e2x-12x2+x   As we know that; The Chain Rule: fgx'=f'gx·g'x

Q: A curve is defined by the parametric equations Find the length of the curve from t=1 to the closest…

A: .We have to find the length of curve,

Q: A manufacturer of canned food packages the product in cylindrical tin cans. The volume of each can…

A: Given

Q: Find the equation of the tangent line to the curve x + y² = 4 where the slope of the curve is 1.…

A:

Q: 3. The radius of a cylinder is increasing at a rate of 4cm/sec. The surface area remains constant at…

A: Given

Q: What is the exact value of cos (tan ¹(-1)) 2 -? sin cos 08-¹(- +/-))

A: We have to find the exact value of costan-1-1sincos-1-32.

Q: A rectangular field is to be fenced off along a river where no fence is needed on the side along the…

A:

Q: Correct Use the midpoint of each subinterval for the value of each ck to find the Riemann sum Ss for…

A: Given f(x) =7-x    ; [-7, -2]   and   n=5

Q: -2x let f (x) = 3x · e¯¯

A:

Q: These points exist on the unit circle: P(-1/2 ,-√3/2) and N(√3/2 , 1/2) Questions: if an object…

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Q: Can someone convert the final answer to integer or decimal?

A:

Q: 13. Algebraically determine the values of that satisfy the equation 2 cos²0+ cos 0-1=0, where 0…

A: First I have let x=costheta And then reduce the trigonometrical equation into algebraic equation and…

Q: 12. A pie is re take the p

A: NOTE: Refresh your page if you can't see any equations. . Newton's cooing law is given by here we…

Q: Find the derivative of the function f(x)=(sqrt(x-1)^2))/x^2+1)

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Q: 0 1 xdx x4 + 1 || T-8 π

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Q: A stone is tosse long will it take

A: Please refer to the image below

Q: 1. Given the function f(x)=2-4x+ -. Please find the intervals of increase or decrease, absolute…

A: SOLUTION-

Q: Which of the following is NOT an improper integral? 0 2x of ₁7² +²22-3²² dx + 2x - 3 2x x2 2 - 3x e…

A: which of the following is not an improper integral??

Q: The polar equation 9 cos 0 + 2 sin 0 = X + 1 9x + 2y 1 9y + 2x = 1 9x + 2y = x² + y² || || 1 - r in…

A: To find  the cartesian form of the given polar equation.

Q: 1) Find the volume formed by rotating the region enclosed by: x = 3y and y³ = x with y ≥ 0 about the…

A: answer is in next step . please give a like!!!

Q: Let 7' (t) = Find a parametric equation of the line tangent to r(t) at the point (59, 0, - 2.303)…

A: Follow the procedure given below.

Q: 11. Ay≈ f'(x) dx III. y2y₁ f'(x) dx - Oll O III O None of the choices OI

A: Using definition of derivative

Q: A lighthouse is located on a small island 4 km away from the nearest point P on a straight…

A: Given problem:- A lighthouse is located on a small island 4 km away from the nearest point P on a…

Q: (a) In the accompanying figure, the area of the triangle ABC can be expressed as area ABC-area…

A: Let's solve for area of the triangle.

Q: Calculate the discount on one bike if they decide to buy 10 bikes at the same time.   1.3.2…

A: This is basic algebra problem

Q: 5. Find Oz дz дх and if x - z = arctan(yz) defines z implicitly as a function of x and y. ду

A:

Q: Solve the problem. Find the area between y = (x - 3)ex and the x-axis from x = 3 to x = 7. A) e²-e³…

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Q: 6. Evaluate the following limits: 1/3 (x+8) -2 a. lim X x-0 b. lim x→-3 2 x²-9 2x² +7x+3

A: Given :limx→0x+813-2xlimx→-3x2-92x2+7x+3

Q: (x + ex sin y) dx - (y + e-x cos y) dy = 0

A:

Q: i) Consider the double integral I = -ff₁₂² Le e²² dx dy. y/3 Draw the region of integration then…

A: Given problem:-

Q: At JCS Construction Plant, cement mixture is falling off a metal conveyor and onto an inverted…

A: Given query is to find the rate of change of height.

Q: Answer the question. x2+1, -1sx<0 0<x<1 5x, f(x) = -3, x = 1 -5x + 10 1<x<3 4, 3<x<5 d -6. 6.S... L…

A: Topic:- function and it's continuity

Q: Which x-value is most useful in approximating log₁0 88? 0 90 O 100 O 10 02

A: Here, to approximate: log1088

Q: Evaluate the line integral, where C is the giv z² dx + x² dy + y² dz, C is the C

A: See the details solution in below

Q: Suppose a model for the surface area of a human body is given by S = 0.1094w0.425,0.725, where w is…

A:

Q: Which of the following integrals are improper? (Select 3 L₁x²-1 dx 3x - 1 1 06²/21 x ² = 1 dx 2x 00…

A: Topic:-  improper integration

Q: Consider the series + ++4+4+.... Does the series converge or diverge? Select answers from the…

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Q: The Cartesian coordinates of a point is (4, - 4√3). This point in polar coordinates can be…

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Q: the convergence and divergence of the following S vergent series. b) Σ=13*51-n

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Q: Show that (cos 0 + i sin 0)" = cos n0 + i sinne for n = 3 and n = 4.

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Q: x² dx x²-3x+2

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Q: 1) In medieval times there were 10,000 people living in a city that was struck by a plague so that…

A: This is a problem related to differential equation. based on the general formula of decay law we…

Q: Find the volume of the indicated region. the tetrahedron cut off from the first octant by the plane…

A: Let's find volume.

Q: Find 넥 L -TS (s+1)e- s² + 4s + 4

A:

Q: Question 1 Approximate 3.92√3.9 without using a calculator. Use the methods learned in class. Do not…

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Q: The given rectangle has a perimeter of 120 cm. Find the values of x and y that result in a maximum…

A: Consider the rectangle

Q: Solve for y esec(4y²-6y+14) = 3x + 1

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Q: Find the area of the shaded region. y = +3 (0,3) (2,7) A) 25/3 B) 352/3 C) 26/3 D) 22/3 2 x

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Q: 3. Consider the function Prove that f'(0) = 0. f(x) = [2³ -2³ if r EQ if x # Q.

A:

Q: The following five statements, numbered 1 to 5, were made about the graph of = tan c. Statement 1…

A: