For the following exercises, draw the region bounded by the curves. Then, find the volume when the region is rotated around the y-axis. 1 x = 0, and x = x +1 88 y = 2

Q: Consider a polynomial f (x) = ax³ – bx +c. Find the value of b if f' (2) = 0 and fl" (2) =44. -

A: The solution is given in the next step.

Q: To improve her handwriting, Hope practices writing the numbers from 1 to 200. How many times will sh...

A: We have considered numbers 1 to 200 in two class. The first class is from 1 to 100 and the second cl...

Q: 1. For the function g(t) whose graph is given below, state the value of each, if it exists. If it do...

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Q: Linear Differential Equations (19) + 3x?y =

A: First I have written the standard form of first order linear differential equation and then using th...

Q: a) Queen Beyoncé's yacht will be leaving from Port Destiny and traveling on a straight line to an is...

A: Given: Queen Beyoncé's yacht will be leaving from Port Destiny and traveling on a straight line to a...

Q: Question Evaluate the following limit using L'Hospital's rule. lim (x+ 6) In ( (æ + 6)² ) z-6+ Provi...

A: if the limx→af(x)g(x) is of the form ∞∞ then by L'Hospital rule the limit is equivalent to limx→af(x...

Q: Proof 2: 14 sin x dx tan xdx = /6 COs x 1 -= sec x dv = sin xdx cos x du = sec x tan xdx v =-cos x 1...

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Q: C. Assessment/Application/Outputs (Please refer to DepEd Order No. 31, s. 2020) Direction: Solve the...

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Q: Homogeneous Differential Equations (13) (4x* + x³y + y*)dx + x*dy = 0

A: We are asked to solve the homogenous differential equation   

Q: Homogeneous Differential Equations (11) (x – y)dx + xdy = 0 (12) (x sin- y cos) dx + x cos 2 dy = 0 ...

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Q: Find the domain and range Vx+1 1- y = 7 х-1 2 - y

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Q: Find y''' (3rd derivative) of y = sin^2 (tan(6e^x))

A: Here,              We have given a function and we have to find its 3rd derivative.         So , the...

Q: Determine whether the integral is convergent or divergent. 1 5 dy 4y - convergent divergent If it is...

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Q: Find the derivative of f (x) = (4x + 1)(5² + ®/æ ). Upload your work in the next question. The deriv...

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Q: There is a large mixing tank that initially holds 120 gallons of brine (water in which salt has been...

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Q: 3. Construct a table of values to investigate the following limits: 10 a. lim T→3 x – 2 10 b. lim T→...

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Q: Question 4 The inventors of Calculus were Sir Isaac Newton and_ A Friedrich Gauss B) Gottfried Wilhe...

A: Carl Friedrich Gauss is known for his contributions to number theory, geometry, probability theory, ...

Q: State the name of the property illustrated below. 4. /8 = /8 •4 Choose the correct answer below. Ass...

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Q: After 2 hours, the population of a culture of bacteria has increased by 50%. If the rate of growth i...

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Q: O convergent O divergent

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Q: IT sin't cos*t d t

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Q: 4. Use the graph to find the following characteristics of a polynomial? K/5 4) Use the given graph t...

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Q: For what Values Of X IS tne wing geommetric series convergent? 1++ 27 1) x>0 2) -1<x<1 3) -3<x<3 4) ...

A: Topic:- series   

Q: Question 10 1+ cost = | cor*rdt cot'rdt I- rost

A: integration

Q: 3. Find the Scalar eguation of the plane containing the line rt) =<!,2,-37+ -3,2, 17 and the point P...

A: Given problem:- Find the scalar equation plane containing the line  r (t)= &lt;1,2,-3 &gt; + t &lt; ...

Q: Determine the form of a particular solution of the differential equation y" + 9y = e*cos3x + x² + x³...

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Q: B Given that V · W = 4, V x w = ,V] = 10and |W = 8. The exact numerical value value of 2V (3V-2W) is...

A: We need to find b,c,d,e.

Q: Theorem 1 Sequence Defined by a Function Let f(x) be a function defined on c, o] for some constant c...

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Q: Suppose the sales tax rate of Pagadian City is 7% of the purchase price. If the price of the digital...

A: Topic:- parsentage   

Q: Find the slope of the line tangent to the curve x + sin(y+π) = 2x3 + ey at the point (-1,0). Show wo...

A: Topic:- application of derivatives

Q: 3. Find the exact value of each trigonometric function. cos-1 cot

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Q: 4 x2-4 xp

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Q: Find the exact value of each expression.

A: For 5:    cot23π4=cot3π4=-1

Q: 1. Using tables of values, determine the limits of the following. (i) lim (x° + 1) x→1 (i) lim(1 – a...

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Q: Find the smallest value of k e N for which the area under the graph of f(x) = x* + x between x = 0 a...

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Q: The curve C is the portion of the graph of y = 16* for 0 <z < 2 (distances measured in m). The curve...

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Q: 2. Evaluate the following functions using the given relations. f(2) = -1 ; Relation: f(n+1) = 5 - [f...

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Q: 1) appropriate (inverse) substitution, i.e. a correctly labeled right triangle: Reduce the following...

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

Q: Problems 24-27 concern g(t) in Figure 2.29, which gives the weight of a human fetus as a function of...

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Q: Vrite out the first five terms of the sequence with, In(n) n+1 determine whether the n=1 sequence co...

A: We will find the limit 

Q: 3. )dx \1+x

A: As per our guidelines we are supposed to answer only one question i.e. the question no (3). For the ...

Q: Solve the differential equation 2xyy' = 1 + y". If y = 3 when x = 2, determine y when x = 1.

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Q: 5. Consider the graph of f (x) shown. Does the lim f (x) exist? Is the function continuous at x=3? E...

A: This question is related to limit and continuity,  we will solve it using given information. 

Q: QUESTION 4 Given f(x) = 8x³ + 2x. Estimate the value of ƒ(2.01) using differential. %3D

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Q: What is the magnitude and direction of the resultant? 10 4. 10 diagram 4

A: Given that:                        

Q: Use a numerical solver and Euler's method to obtain a four-decimal approximation of the indicated va...

A: solution

Q: Country Population Size Number of Eggs Consumed Number of Cattle Area United States 325 millio...

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Q: sec?xdx Evaluate the given function ſ V1-4tanx a.글(1-4tanz) +c ·극(1-4tanx)i + C c.(V1 – 4tanx)' + C ...

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Q: Evaluate the integral. 0.4 x2 dx 4 - 25x2 |

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Q: 1 dy rVx²-9/ -3 dx exVe2x_9,

A: ∫1xx2-9dx