Sketch the region whose area is given by the definite integral. LV16. V 16 - x² dx y 15 10 5 y 4 3 2 X y 8 6 2 y 3 2 2

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A: We know that limit definition for definite integral is  ∫abf(y)dx=limn→∞ ∑i=1nf(yi)Δy Where, for…

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Q: The population of Toledo, Ohio, in the year 2000 was approximately 520,000. Assume the population is…

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Q: 1. Determine whether or not the following relations are functions. If the given relation is a…

A: As per our guidelines we can answer only 1 question, so kindly repost the remaining questions…

Q: 7) Find the first-order derivatives of: (a) y = -7e* (b) y=-3x² (c) y = 를

A: Given; Functions (y) is given.       NOTE: - The first order derivative also represents the…

Q: Find the extreme values of g(x, y) = x² + y² + x²y on the circle x² + y² = 12 using the method of…

A: maximum value=28 minimum value=-4

Q: Equations of Order One: Homogeneous Equations Instructions: Obtain the family of solution of the…

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Q: Find the volume of the solid generated by revolving the region about the line x = 2. The region…

A: volume=16.75 unit cube

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Q: Explain why or why not Determine whether the following statements are true and give an explanation…

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Q: Problem 3. We want to estimate (²1/1 X dx. We will use the right sum, left sum, midpoint rule and…

A: Let's calculate L(2),R(2),M(2) and T(2).

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Q: Find the limit. Use a graphing utility to verify your result. (Hint: Treat the expression as a…

A: Given limx→-∞5x+25x2-x

Q: IV. Given the functions f(x) = 2x + 5, g(x) = -x² - 6x + 7, and h(x) = the following. Show complete…

A: Note:- These are multiple subparts according to company guideline we can do maximum 3 subparts so i…

Q: Let R be the region bounded by:                                              y=sqrt x−4 , x=13,…

A: The objective is to solve the above question.

Q: Find two positive numbers that satisfy the given requirements. (Enter your answers as a…

A: Note:- These are multiple questions. According to guideline we can do maximum 1 so i am solving here…

Q: For the polynomial function f(x) = -x²(x-3)(x + 5), answer parts a through e a. Use the Leading…

A: Concept: A mathematical phrase, rule, or law that establishes the link between an independent…

Q: Find dy/dx when 1. 2. 3. 4. 5. dy dx dy dx dy dx dy dx dy dx x³ + 2y³ - 9xy - 1 = 0. x² - 3y X 2y² +…

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Q: dx dy A point is moving along the graph of the given function at the rate Find (in cm/sec) for the…

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Q: The series is absolutely convergent on the following interval. x-5 <1 |x - 5] < 10 x € (-5, 15) An…

A: Given series ∑k=1∞(-1)k10k(x-5)k

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Q: . y = sec(x)√1+cot² x csc³(x)

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Q: f(x+h)-f(x) h 2. Find f'(x) using f'(x) = lim h→0 a) f(x) = x+2 for one of the following functions:…

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Q: MULTIPLE CHOICE 1. Let f(x)=x-g(h(x)) where g(4) = 2, g'(4) = 3,h(3) = 4, and h' (3) = -2. Find ƒ'…

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Q: The population of a town is approximated by the function 90000(1.02)', where t is the number of…

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Q: explain why the graph is discontinuous at x=1 1= { * 1 f(x) = X²-X IF X 1 if X = 1 X²-1 Sketch the…

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Q: Given U₁ = = 0 (93).- (3). = - (²) (₂). 0₁ = = (-²) U4 , V3 = peform the indicated operations

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Q: c+1 for all real numbers E cical points is negative and the ver is not an integer or with am pe no…

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Q: Use a linear approximation to estimate (0.99

A: Linear approximation is given below

Q: The surface area of a right-circular cone of radius r and height h is S = Tr√√² +h², and its volume…

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Q: 3 - 6x IV. Given the functions f(x) = 2x + 5, g(x)=x² - 6x +7, and h(x) = == -, evaluate x-4 the…

A: Note: as per guidelines we support only three subparts of the questions.kindly repost next questions…

Q: Consider the position vector of a moving particle. r(t) = (e-³t sin(t), e¯ -3t cos(t), 5e-3t (a)…

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Q: 10 sin(0-5) 0-5 02-20-15 6. Find lim

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Q: what is df=

A: As you ask about df so i am only defining it.

Q: For the part of the solution to the DE shown below, y ln x ln y dx + dy = 0 [y ln x lny dx + dy =…

A: The given part of the DE is ∫ln x dx+∫dyy lny=0 We have to find the next step of the DE

Q: Equations of Order One: Separation of Variables Instructions: Obtain the general solution of the…

A: Given, mydx = nxdy

Q: and the condition y(0) = 1. y(t) = e^(t^2)(1+2t^3) dy dt -2ty=-61²e¹²

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Q: y = y" x Express y" in terms of x and y. (Use symbolic notation and fractions where needed.)…

A: Topic:- calculus

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A: Make a right angles triangle. Assume Sin-1(x)=y and equate perpendicular and hypotenuse side of the…

Q: The solution to the DE (1+x) dy -y dx =0 is O a. y = C (1+x) O b. y = c (1-x) O c. x = C (1+y) O d.…

A: Given: So,                (1+x)dy-ydx=0⇒dydx=y1+x⇒dyy=dx1+xIntegrating both sides we get,⇒ln y=ln…

Q: 4. A farmer has 80 hectares of his farm available for planting maize and cabbages. He must grow at…

A: Total land= 80 hectares  Let, a hectare for maize and b hectare for cabbage.

Q: g) (sin x)² = 4 — 2(cos x)², with 0 ≤ 2 Vair

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Q: Consider the solid generated when the region enclosed by y = √, y = 2 and x = 0 is revolved about…

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Q: d³y 1) Find the order and degree of the differential equation: + dx³ 3d¹y dx4 = dy 4xy dx

A: Since you have asked multiple questions in a single request we would be answering only the first…

Q: ft A ladder leans against a vertical wall. If the top of the ladder slides down at 2.5- elevation of…

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Q: 3) An oven is preheated and then remains at a constant temperature. A potato is placed in the oven…

A: Concept: Given the equation to represent (T) temperature at a given time t Putting the values of (T)…

Q: A weight of 1200 pounds is suspended from two cables as shown in the figure. What is the tension in…

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Q: d) e) V₁.0₁ U4 = 0₁.03= V3 Round your answer to 3 decimal places. Round your answer to 3 decimal…

A: v1→=108-4=10i^+8j^-4k^v2→=-8-6-7=-8i^-6j^-7k^v3→=-13-9=-i^+3j^-9k^v4→=-7101=-7i^+10j^+k^