Prove, using integration, that the volume of a sphere with diameter "d" is πYd³ 6

Q: Which of the following statements is (are) false? A) A basis is a spanning set that is as large as…

A: Please see the below picture for detailed solution.

Q: A. Find the following limits. Answer four only. x-¹-1 i. ii. iii. lim- X-1 X-1 lim 4x-x² X-4 2-√√x…

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Q: .2 .4 S 7 iti ti ti ti 1+ -14 ។ 11 2

A: it is very basic question of complex number.

Q: The radius of a right circular cone is increasing at the rate of 6cm/sec while  its altitude is…

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Q: (g) Determine the minimum or maximum value of the function. (h) Write the domain and range in…

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Q: Q5: Find for the following functions: (1) In(x - y) = xy + y³ (2)y=tan³ √/cot(7x); (4) y = x sinh…

A: Solution is given below:

Q: (B): Find the tangent equation to the curve y = sin² x at point x =

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Q: Compute the indefinite integral of the following function. r(t) = (13 cost,7 cos 5t,3 sin 6t)

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Q: 18. Assume that f"(x) = (x + 2)²(x-2)(x - 3)(x - 5)³. Find x-value(s) for all inflection point (s).

A: If sign of f''(x) changes when we move from left to the right of x=a then x=a is known as the point…

Q: Describe the domain and range of the function. F(x, y) = 5x² - y Domain: 0 {(x, y); x = 0} 0 ○ {(x,…

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Q: 4. C(x-xxx

A: 4. ∫-342x5-3x4+4x3dx Note:    Multiple questions are given, we are answer only one question. If you…

Q: 3. Solve one of the following inequalities. Write your answer as an interval or union of intervals.…

A: This question is based on finding solution of inequality.

Q: Exercise (b) the centroid of the region bounded by the graphs of the equations Step 1 The region is…

A: Please see the answer below.

Q: (1) In(x - y) = xy + y³ ;

A: According to rules, I need to solve first question.. Please repost remaining questions

Q: Suppose that f is integrable on [-4, 7]. If the average of f on the interval [-4, 7] is 4.25, fin 4…

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Q: Q2: Solve the following dx 7x³+14x+15 (x+3)(x+7) 1735 (1) J inte (2

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: Question 5 Test the series below for convergence using the Root Test. 5)₁ ∞ n=1 f(n): 3n 6n + 5 The…

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Q: -1 t² Vta 6 dt

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Q: ¡¡y y cos x² dx dy Evaluate the double integral by reversing the order Show your answer in details.

A: Change the order of integration and then  change limits respectively

Q: 2. Approximate 64.1 by using linearization and use a calculator to compute the percentage error.

A: Given :64.13

Q: The graph of y = f(x) is shown. Use the graph to answer the question. Find lim x-(-1)- O-2, -7 O-7,…

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Q: (g) Determine the minimum or maximum value of the function. (h) Write the domain and range in…

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Q: If A, B, and C are 3×3 matrices; and det(A) = 5, det(B) = −2, and det(C) = 3 then compute: det…

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Q: Given the function f(x) = x² – 3x f(2+h)-f(2) h (a) Find the expression (b) Use your result from…

A: The given function is ; f(x)=x2-3x.

Q: Use the figure below to find the exact value of the trigonometric function of angle A. sin(A) 00 7 A

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Q: 38.Calculate the surface area of the surface obtained by revolving the curve y = √9-x² around the…

A: Note to student :    Thanks for posting your queries. But there are multiple questions given. As per…

Q: -2y²z3,-4xyz3, -6xy²z²)

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Q: Find f(145) (x) for f(x) = 83x¹0⁹. Simplify your answer completely. f (145) (x) =

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Q: Q2: Solve the following integrals: (3) √ √dx dx (4) fxe* dx

A: The objective of the question is evaluate the indefinite integrals.

Q: Use the substitution u = 3x²-2 to find the following indefinite integral. Check your answer by…

A: We need to find integral.

Q: (B): Find the unit vector 3i - 4j + 5k perpendicular to the vectors: 4i + 5j-6k

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Q: Q1: Fill in the blanks for the following statements (chose five only) 4n 1. lim→∞ 2n+1 log10 (3x -…

A: The objective of the question is fill the blanks.

Q: Given that 0. ∞ n=0 x = 1 1 <- x to x = = Identify its interval of convergence. The series is…

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Q: Find S н - 2+ dx

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Q: Find the order 3 Taylor polynomial T3(x) of the given function given. Use exact values. 6 f(x) = (5x…

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Q: (1) Find the Taylor series for f(x) centered at the given value of a. (Assume that f has a power…

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Q: Solve the initial value problem 25y" - 40y' + 16y = 0, y(0) = 2, y'(0) = 3. y(t) = How does the…

A: We have to solve the initial value problem 25y'' - 40y' + 16y = 0 y(0) = 2 &amp; y'(0) = 3

Q: Q5: Find for the following functions: dx (1) In(x - y) = xy + y³; (2)y=tan³ √/cot(7x); cash? -nh.…

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Q: sin 8 cose √cos²0-9 c. f S do

A: Since, we have been asked to solve Part-C in which we have to evaluate the integral given…

Q: 5. Find the volume of the solid by the shell method. The solid is obtained by rotating the region…

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Q: Evaluate the integral and check your answer by differentiating. x8 + 8x5 x7 1 dx +C

A: Firstly expand the fraction of given Integral and then integrate

Q: X y = x + Ae^ + Be - 2x

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Q: Q2: Solve the following integral (1) 7x²+14x+15 (x²+3)(x+7) dx dx ; (2)

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Q: , 4x²+x+17 (x+1)(x²+4) dx I

A: Hee, to evaluate the given integral we have to rewrite the rational function.

Q: Find the absolute maximum and absolute minimum values of f on the given interval. a)…

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Q: A cylindrical tube expands as its radius r and height h increase at the rate of 2 in/min and 4…

A: Basic product rule of differentiation is used.

Q: First, compute the gradient of the function f(x,y) = 4+5x²-3y². Then evaluate it at the point…

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Q: Skill Building In Problems 13-24, use the graph on the right of the function f. 13. Is fincreasing…

A: Please see the answers below.

Q: dw (C): If w = tan x and x = 4t³ +t; Find dt

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Q: (18) Find the derivative of the functio 2²+5 3 Y=2²-5 Nor me it to Vitou inst

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