How do you solve related rate problems in calculus? List all steps.

Q: Suppose there are 10 points in a plane such that no three points are collinear. How many distinct…

A: Given; There 10 points in a plane such that no three points are collinear

Q: 11. Rules of Definite Integrals: I f(x)dx = 6, and "f(x)dx = 4 , find the following: a) c)

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Q: Find y if y= 3(x³ – 7x+2)5 +4x -2.

A: Topic = Derivative

Q: it is always that when the series equal to zero it converges and when it is nonzero it diverges ?

A: For a series to be convergent we must have limn→∞an=0. But the converse is not true.  For example:…

Q: 5y² = 2x³ – 5y

A: Derivative with respect to x

Q: For each problem, use implicit differentiation to find dy/dx in terms of x and y.

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Q: Use a graph to determine whether the given function is continuous on its domain. H Sx + 2 if x < 0…

A: Given query is to find function is continuous not.

Q: can you check up the answer? it is not right

A: I have rechecked the work using calculator. It is correct.  Using calculator I have got: limn→∞…

Q: C. 5x' + xy = 5x°y³ .3 ху .3

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Q: Determine the convergence or divergence of the series. n = 8 converges diverges

A: Given query is to find series converges or diverges.

Q: 2. f(x)= 7x2 -19x - 6 at (4, 8)

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Q: x² – 2x – 1 dx (x – 1)2(x² + 1)

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Q: Test the series for convergence or divergence using the Alternating Series Test. 00 (-1)" 3n + 1 n =…

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Q: f (x) = sec? x +1

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Q: Consider the following series. n In(n) n = 2 Does the function f(x) satisfy the conditions of the…

A: This is a problem related to series and sum calculation. By evaluating integral we will answer the…

Q: Finding the Area Bounded by Two Graphs Sketch the region bounded by the graphs of the functions. See…

A: This is a problem related to area of the intersected region by given curves. Based on the general…

Q: Test for convergence or divergence, using one of the tests listed below. 1 1 n + 5 n + 6 n = 1…

A: Given query is to find series converges or diverges

Q: dy Find for y = dx V7 – x2 dy dx

A: Differentiate  y with respect to x

Q: 8. Between 0°C and 30°C, the volume V (in cubic centimeters) of 1 kg of water at a temperature is…

A: density=massvolume For  density to become maximum, volume needs to be minimum. Given

Q: Give the generator, the directrix, and the rulings of the cylinder x = lnz. Draw a sketch of the…

A: We need to give generator, the directrix, and the rulings of the cylinder x = lnz.

Q: goo3D 4X Sxt7

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Q: Sketch the graph of the following equation 2x + 6y + 3z = 12

A: To sketch the graph of given equation

Q: x + 1 S dx (x² +2)( x² + 1) 2

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Q: g(x) If f(x) then h(x)'

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Q: dx sin x

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Q: Consider the following series. 8 + e-n n = 1 What does the Test for Divergence reveal about this…

A: We know the necessary condition for the convergence of a series. A series ∑nan   is convergent…

Q: Consider the graph and determine the open intervals on which the function is increasing and on which…

A: Here to of the function is at point (1,5), On left side function is increasing ,and at right side…

Q: 25 18 f(x)dx f(2)dæ = / f(x)dx - 10 where a = and b =

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Q: Determine whether the infinite geometric series is convergent or divergent. If it is convergent,…

A: Given query is to find series converges or diverges.

Q: Given the function graphed below, evaluate the definite integrals. 4 3. -1 1 2 3 5 -1 -2 -3 -4 1 |…

A: We have to find the value of the integrals.

Q: Find an equation for the hyperbola that satisfies the given conditions. Vertices: (±1, 0),…

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Q: dy/dx + 2xy + xy = 0 Ans. 1/y3 = -;+ 1 + ce3x? 2

A: The given differential equation is  dy/dx + 2xy +xy4=0

Q: Directions: Prove the following statements. 1. If f(x) = (x² – 1)3 then f'(x) = 6x3 – 12x + 6x.

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Q: Use a graph to determine whether the given function is continuous on its domain. [3 – x if x 3…

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Q: Find the area bounded by tHe curves y=8x-x and y= 3x

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Q: i=1 + 20b;)

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Q: Use the product rule to find the derivative of (- 72° – 4x10) (5e² + 4) | Use e^x for e". You do not…

A: This question is related to differentiation, We will solve it using given information.

Q: The shaded region shown below is bounded by the functions f(x)=−x2+10f(x)=−x2+10 and…

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Q: Find the arc length L of the graph of r(t). r(t) = 2 cos(t)i + 2 sin(t)j + tk, 0<t< 2n L =

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Q: Evaluate the following integrals? .3 1)S x² e3* dx 2) S dx x²+25 dx 3) 6x – x2 4) | cos(In x) dx

A: “Since you have posted a question with multiple sub-parts, we will solve first three subparts for…

Q: Write the sum using sigma notation: 8 + 12 + 16 + 20 + ...+ 36 = ) B, where n=1 A = B =

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Q: Evaluate the integral (Trigonometric Substitution) x*dx (x² + 9)2

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Q: 8. S 3tan 3z r sec? 32 da

A: As per the guidelines I can solve only first question

Q: Convert the differential equation x''' = x'' – 2x' – 4x +t into a system of first order equations by…

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Q: 12. Determine the work done by the force, F, in the direction of the displacement, 3. F| = 350N 10…

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Q: Determine if the geometric series converges or diverges. If it converges, find its sum. 24 3 4 + 1+…

A: Given query is to find series converges or diverges.

Q: 00 Σ 2 ni(6x – 1)" n = 1 R = Find the interval, I, of convergence of the series. 1. OI = 1%3{1} O I=…

A: Series

Q: If 1234 cm? of material is available to make a box with a square base and an open top, find the…

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Q: If a rock is dropped from a height of 45 ft, its poistion t seconds after it is dropped until it…

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Q: e cos xy [ydx + (x + tan xy) dy] = 0 %3D

A: