Derivation of a formula of volume cone (using Calculus, in two different ways).

Q: Find the indefinite integral in each of the following. Show all necessary solutions. 3. sin ? x cos'...

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Q: Express the repeating decimal as a fraction. 0.685828282828... 0.685828282828...

A: This question is based on conversion from repeating decimal to fraction.

Q: Find y'' by implicit differentiation 4x3+3y3=6

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Q: Find the volume of the solid obtained by rotating the region below the graph of y = e-2x about the x...

A: Given problem:- Find the volume of the solid obtained by rotating the region below the graph of y = ...

Q: Given f: [2, )IR, prove that fn (x) = けx" It, converger uni formly to f6)-o.

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Q: Find the derivative of the folowin g tetion 5(tansc) BIY= Tin1o](Sin )C cosse) Cy'= Dy= %3D Sn( cot>...

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Q: x2 - 2x + 1

A: The expression to calculate the the antiderivative of the given function: Fx=∫fxdx   The Power rule:...

Q: 3. x/1+ x6

A: here you have mentioned to solve this integral by Integration By Parts.  

Q: 15 What is the exact value of tan (sinr) where r 17 Provide your answer below:

A: Solving the problem by finding the value of the function.

Q: Find the cross product ax b: a=(2, – 1, 2), b=<0, 4, 5)

A: Given that: a=&lt;2, -1, 2&gt;b=&lt;0, 4, 5&gt;

Q: Consider the differential equation e' (3x-6x). Let y = f(x) be the particular solution to the differ...

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Q: Suppose the weekly marginal revenue function for selling x units of a product is given by the graph ...

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Q: 3) Use the method of cylindrical shells to find the volume generated by rotating the region bounded ...

A: This question is based on cylindrical shell method integration.

Q: 1. Find the values of x,4 and z that corvespond to the critical point of the funchion Z="f(x,4)= Sx?...

A: We have to find critical points of f(x,y).

Q: An initial investment amount P, an annual interest rate r, and a time t are given. Find the future v...

A: P=$350 r=0.0272 T=12years Formula used A=P((1+(r/n))^(n*t))

Q: Express w as a linear combination of u and v: ? = (4,1), ? = (−2, −1), ? = (2, −2)

A: Let w = (4,1) u = (-2,-1) v=(2,-2) we can write this as: u-21 + v2-2 = 41   -2u + 2v = 4 u - 2v = 1 ...

Q: Consider the following function. +] - 2x + 2 3 2 (a) Find y'-f"(x). "(x) = (b) Find the critical val...

A: Topic = Derivative As per guidelines , At  a time only three sub-parts can be answered.

Q: The graph of f (x) is given by Determine the following limits. Write your answer in the form lim f(x...

A: Topic = Limits

Q: integral f (z+1) e^2z  dz

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Q: Test the series at the given values of x for convergence or divergence. (x+2)" Σ n=0 7" (3n + 1) • T...

A: Given the series is ∑n=0∞ (x+2)n7n (3n+1)

Q: Test each of the following series for convergence by either the Comparison Test or the Limit Compari...

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Q: Test the series for convergence or divergence. 1.9. 17 · 25 7. 12 · 17 · 22 1 1.9 1.9. 17 + 7. 12 · ...

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Q: Solve each triangle. Nearest tenth.

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Q: y= 3x³etan ( – 4x)

A: Topic:-  derivatives 

Q: 2. (D+7)°y = 0

A: Hope you are asking for question number 2 in part C  I am answering it here.

Q: 2. Use central difference approximations to estimate the first and second derivatives of y = e* at x...

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Q: Show that the coefficients of the given differential equation are homogeneous and solve the give dif...

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Q: Find the point (x,y), at which the graph of y = 8x + 9x - 7 has a horizontal tangent. The function y...

A: Given that: y=8x2+9x-7

Q: What is lim1 f (x) ? X

A: Find your answer below 

Q: Let (M; d) be a metric space. Show that the set {B(x; 1=n); x ∈ M; n ∈ N*} is a Basis for the metric...

A: Given :  (M; d) be a metric space. To Show :  the set {B(x; 1=n); x ∈ M; n ∈ N*} is a Basis for the ...

Q: Evaluate the following expression. arccsc(/2) Provide your answer below: Radians

A: We can find the answer as below.

Q: Suppose that in winter the daytime temperature in a certain office building is to be maintained at 7...

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Q: Find the Taylor polynomial of orders 0, 1, 2, and 3 generated by f at a. 2n f(x) = cos x, a= Po(x) =...

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Q: A. Ellipse B. Parabola C. Hyperbola

A: Given that: f(x, y)=9x2+4y2

Q: Evaluate the following expression. arcsec (2) Provide your answer below: Radians

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Q: 19. Identify the critical points and the inflection points of (x) FX) = (x - a)(x + a)', for a > 0. ...

A: The given function f(x)=x-ax+a3

Q: Use the formula for the sum of a geometric series to find the sum or state that the series diverges....

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Q: Differentiate f(r)= tan(3x). Use exact values. f'(x) = %3D

A: Given ,f(x)=tan-1(3x)We know that, ddx(tan-1(x))=1x2+1Differentiate w.r.t. xApply chain rule,f'(x)=1...

Q: The table below gives data from a linear function. Find a formula for the function. Year, t Value of...

A: We have to find the linear function.

Q: Evaluate the integral S - dx V16-x2

A: Evaluate the integral of the integrand  x2/√(x2-16) .  

Q: Find the abs extrema as well as all values of x where they occur for the domain.   f(x)= x/12 + 1/...

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Q: (a) Find the series' radius and interval of convergence. Find the values of x for which the series c...

A: The given series is: ∑n=0∞ nxnn+10

Q: f(x) =sin x. 1) find f'(x). Second, Third, and Fourth derivitive.   2) What is f^(4n)(x) when n i...

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Q: If s(t)represents the position of a function, in metres, at time t, in second what does the expressi...

A: s(t) represents the position then  limh→0s(3+h)-s(3)h represents the velocity at time t=3 seconds Co...

Q: for a sum of $8000 to double in 12 years and 9 months, what must be the rate of interest compounded ...

A: The solution is given in the next step.

Q: This answer is not correct

A: Given that: limt→09t1+t-9t

Q: Find: Wx-Wy,Wxy Way, Wxx Wyy,Wz, Wzz Wzx, WZy Wyz, Wxz W= sinh (xy-2) %3D

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Q: Let y be the part of the curve y = x² running from (-1,1) to (2,4). Calculate xy dx + (x + y) dy.

A: (1)

Q: If f(x) = 2 tan '(5 sin(3r)), f'(x)-

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Q: Evaluate the ff: 23 D S fda, given f 6)- and acx) F 1 3+3 X

A: Let's find.