Find the approximate increase by the use of differentials, in the volume of the sphere if the radius increases from 2 to 2.027

Q: Find the slope of the tangent line to the graph of f(x) [Α] Ο [B] 1 [C] -1 [D] ¹ [E] 1 = √= x+

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

Q: 9x 2 dx ,2

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Q: Find the arc length of the following curve on the given interval. x = 71³, y=21², osts √/3

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Q: Sexy² dx + 2x²ydy where C is the triangle with 7) Evaluate vertices (0, 0), (2, 2) and (2,0)

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Q: Solve the following maximization problem graphically. Subject to: P(x, y) = 38x6y + 14 x + y ≤ 10 2x…

A: To solve the following maximization problem graphically.Px, y=38x-6y+14 subject to:…

Q: Find a formula for the general term an of the sequence assuming the pattern of the first few terms…

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Q: Please Rewrite this so I can understand

A: Solution

Q: Evaluate the integral f25 (2-6) dx by making the substitution u = -6. + C

A: Given integral:- ∫x5x6-67dx

Q: $1₁² f(x) dx = -3₁ ["* fo If 1. [² f(x) dx = 2 /*18(x) + 2] dx = f(x) dx = 10, and [8(x) g(x) dx =…

A: If ∫-24fx dx=-3, ∫24fx dx=10, and ∫-24gx dx=8, then to find the following integrals.1 ∫-22fx dx=?2…

Q: Water leaking onto a floor forms a circular pool. The radius of the pool increases at a rate of 4…

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Q: Find the interval of convergence for the given power series. n¹¹(x +11)" 11 35 n=1 (5") (n ³ The…

A: Let's find interval of convergence.

Q: The expression A CSC X sin²x + cos²x sin x is equivalent to C sinxcot x

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Q: Find the surface area of the part of the sphere x² + y² + z² = 64 that lies above the cone z = √√x²…

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Q: (c) To find the distance across a river, a surveyor chooses points A and B, which are 10 ft apart on…

A: Given: ∠BAC=105°, ∠ABC=45°, AB=10 ft

Q: 6. (y-x + xycotx) dx + xdy = 0

A: Note: Since, the student has mentioned to solve question no. 6, so we are solving according to…

Q: Sin (12) २ गठ }}

A: Given expression is sin-1-22   Applying the property of inverse trigonometric functions:…

Q: Sat) Evaluate the integral using an appropriate substitution. x√1-x dx = + C

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Q: xy' + y = x² - 3x

A: xy'+y= x4-3x

Q: f(x, y) = e³y - 6ye⁹x Local maxima are Local minima are Saddle points are ww ww

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Q: (e) Sketch the triangle and then solve for all missing values in the triangle using the Law of ZA…

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Q: Find lim (x,y)-(0,0) y7x⁹8x97y8 + x105 xy7 +x8

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Q: A cone is to be fixed at a certain volume. If the height of the cone changes, then the radius also…

A: Product  rule of differentiation:

Q: 18 12 [th* f(x)da – [." f(x)da - ["f 2 2 a where a = and b = f(x) dx

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Q: Find the integral. Show work. fx¹nx dx 25 (51nx-1) + C 1 25 (lnx-1)+C Ox++0 x(51nx-1)+C

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Q: Find the sum of the series: 2-2 sin (2) n=0 X (-1)"16"-1 2n + 1

A: Solution: ∑n=0∞(-1)n·16n-12n+1 If there exists an N so that for all n≥N, an≠0 and limn→∞an+1an=L if…

Q: Express the limit lim n→∞ a = n Σ (7(x)² - 4(x) ³) Ax; over [5, 8] as an integral. i=1 Provide a, b…

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Q: Solve the given differential equation. 5x4cos² ydx-dy = 0 (A) y = tan (x5 + C) (B) y tan-1 (x5 + C)…

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Q: The Taylor series for f(x) = x³ at -3 is Σ c₂(x + 3)". n=0 Find the first few coefficients. CO C1 C2…

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Q: 6) Show that (2xy, 2yz + x², y²) is conservative.

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Q: f(x)=2x^2

A: given function is f(x) = 2x2+9x+92x2-5x+3   then finding following :--   (1)  finding y - intercept…

Q: Consider the indefinite integral 2³ · √zª + 9 dr: This can be transformed into a basic integral by…

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Q: Assume y is related to x through the differential equation: a =b-y dy dx where a = 0.2, b = 1.4,…

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Q: Find the extremum of​ f(x,y) subject to the given​ constraint, and state whether it is a maximum or…

A: To find the extremum of​ fx,  y subject to the given​constraint, and to state whether it is a…

Q: x5 (26 + 6)6 This can be transformed into a basic integral by letting Consider the indefinite…

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Q: Use the formula for the general term (the nth term) of an arithmetic sequence to find the sixth term…

A: As we know  General formula of arithmetic sequence ⇒an=a+n-1d ⇒a=first term ,d= common difference ,…

Q: 5- Find 3 geometric means between 7 and 4375.

A: We need to find geometric mean. As per Bartleby guidelines we can solve one question from multiple…

Q: Determine whether the series is convergent or diverge 1 n=1 m² 6n + 12 - www. converges diverges

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Q: function is never increasing or decreasing, enter NA in the associated response area. easing:…

A: We  will find the required.

Q: We are interested in the first few Taylor Polynomials for the function f(x) = 4e + 3e X - centered…

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Q: Consider the function y = (ex+b)x. Which of the following is true? The function is increasing in its…

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Q: In AABC we are given ZA=15° ,ZC = 30° and c=20 in. Find b.

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Q: Find the Maclaurin series for f(x) using the definition of the Maclaurin series. f(x) = xcos(5x) M²…

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Q: Approximate the critical numbers of the function shown in the graph. Determine whether the function…

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Q: S25 =

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Q: Which of the following is true regarding the function y = (ax²+bx+c) ²? The function is increasing…

A: A function f(x) is increasing at x=a if f'(x) > 0 at x=a . A function f(x) is decreasing at x=a…

Q: Find the value of the limit for the sequence given. 1-9-17 (9n+1) 0 -1 I 9n+D)} öö (9n)²

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Q: Find the power series representation for g centered at 0 by differentiating or integrating the power…

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Q: Eliminate the parameter to express the following parametric equations as a single equation in x and…

A: Given: We know that sec2(t)-tan2(t)=1. So,                    sec2(t)-tan2(t)=1⇒y+1-x2=1⇒y=x2

Q: Question 8 Find 3 - 4 (6x5 + 2x²) dx <

A: Solution ⇒    8)  ∫−43(6x5+2x4)dx    We know  ∫(xn)dx=xn+1n+1    so first we will…

Q: (4-6) Determine the area bounded by: 4. y=x³-4x and y = x² + 2x

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