Using the Second Derivative Test, where applicable, find all the relative extrema of f(x) = 12x³ − 45x¹ +80x³ − 360x² + 100. -

Q: 1) Suppose that F(x) = 15x³+4x² - 3x + π. For each of the following questions, type yes if the…

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Q: Suppose R is the triangle with vertices (−1,0), (0, 1), and (1,0). (a) As an iterated integral, ff…

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Q: Let g(x) = x(lnx)². Find the open intervals on which g(x) is increasing and decreasing.

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Q: Two chemicals A and B are combined to form a chemical C. The rate of the reaction is proportional to…

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Q: Let f(x) = √28 - 4x and g(x) = 4x² — 2. • You must combine all like terms before yo your answer. •…

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Q: Find the centroid of the region lying between the graphs of the functions f(x) = ¹ and f(x) = = *CM…

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Q: Evaluate the following integral using integration by parts. f10te' dt OA. 10te¹ + (10te¹) dt OB.…

A: Given query is to find the value of the integral.

Q: Use the Special Integration Formulas (Theorem 8.2) to find the indefinite integral. [√17X 17x² - 1…

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Q: Find the area of the region bounded by the y-axis, the line x=3, and the functions f(x) = (x² - 3x +…

A: We have to find the area of the region bounded by the y-axis, the line x=3, and the functions…

Q: 8. Let y find = dy dx 4x√x² +8 (x +9)2/3* at x = -1. Use logarithmic differentiation to

A: The given data is: y=4xx2+8x+923  Use logarithmic differentiation to find dydx at x=-1

Q: Question 10 Determine the derivative of the given function y = log(a+b) cosh (2³) where a an…

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Q: Consider f(x) = x + 5 and g(x) = 1 x² - 4 • You must combine all like terms before you submit your…

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Q: Find the area of the region bounded by the curve y = x² - 6x + 7 and the line x + y = 3.

A: The curves are y=x2-6x+7 and x+y=3

Q: Find the intervals on which f is increasing and the intervals on which it is decreasing. f(x) = -2…

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Q: C C 7. Find the critical values for f(x) = x² + 4x²³² + 4x² 2. On what interval(s) is the graph…

A: Concept: A function's derivative can be used to determine whether it is dropping or rising on all…

Q: 1. (a) (b) Find and sketch the domain of the function f(x, y) = = Show that x²y² lim (x,y) →(0,0)…

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Q: e think of In(-3x + 7) as In(u), then u is a differentiable function of x and u = tionally, if we…

A: Topic:- application of derivatives

Q: Let r(t) = (t², 1 — t, 4t). Calculate the derivative of r(t) · a(t) at t = 9 assuming that a(9) =…

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Q: Find ff f(x, y) dA where f(x, y) = 3x + 1 and R= [0, 3] x [1,3]. R SSR f(x, y) dA =

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Q: Integrate the given function. 2x S cos ²x dx [cos ²x dx =

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Q: Use the tangent plane to approximate a function of two variables at a point. Use a tangent plane at…

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Q: Solve the given equation.. dy dx a. + 2xy = x, y(0) = -2 C. y(x)= xex-2e-x² ex-5e-x² 2 b. y(x) = 1/2…

A: The given equation is; dy/dx+2xy=x, y(0)=-2.

Q: Are 2 -baz

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Q: Solve the given initial value problem by using Laplace transforms. y" + y = 2, y (0) = 4, y'(0) = 3…

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Q: Given the following differential equation: (y³+ kxy4 - 2x)dx + (3xy² + 20x² y³ - ky)dy = 0 a) Solve…

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Q: Find the interval(s) on which ƒ(x) = |x² − 5x + 15 is differentiable. Enter your answer using…

A: The given function fx=x2-5x+15 We have to find the interval on which fx is differentiable.

Q: Solve (√x+x)=√y+y Select one: O a. y (c(1+√x) + 1)² O b. y = (c(1+√x)-1)² O cy=(-c(1 + √x) + 1)² O…

A: The given equation is; [sqrt(x)+x]dy/dx=sqrt(y)+y.

Q: Please resolve this one.

A: Given integral:- ∫07dxx+13+1

Q: List the first 4 terms of the sequence starting from n=1 n {(-1)^ ^ +1} ₁ n 2

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Q: Given a first-order differential equation: /1 + x² dy-ydx = 0 a) What is the best solution method in…

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Q: Solve the inequality. State the solution in interval notation: x ≤ < 1 - 2x x-2

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Q: Family Tree A person has two parents, four grandparents, eight great-grandparents, and so on. How…

A: Please see the answer.

Q: Question 23 arctan y + ln(1 + y²) =a²x³: Find y': Gaz (1+²) 1+2y O Jamani No answer text provided. y…

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Q: DEFINITION 7.1.1 Laplace Transform Let f be a function defined for t≥ 0. Then the integral £{f(t)} =…

A: Given function is ft=9,    0≤t&lt;30,    t≥3 We need to find laplace tranform of the given function.

Q: Obtain the differential equation of this family of curves. The lemniscate ² = acos 20

A: see below the answer and calculation

Q: Consider the following. 7x²y³ = 8 (a) Find y' by implicit differentiation. 14x 3y y' = (b) Solve the…

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Q: dy 9. Given the curve xy - y³ = 7, find dx y [A] xyz [B] 3y x-y² y [C] -²/3 [D]x-3y [E] y x-3y²

A: On solving this we will get

Q: Evaluate the following integral. 2x + 5 2 x + 25 X 2x + 5 2 x + 25 dx dx =

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Q: In Exercises 9-16 of Section 13.4, you found T, N, and K. Now, in the following Exercises 9-16, find…

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Q: Give the appropriate form of the partial fraction decomposition for the following function. 5x (x -…

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Q: Question 9 Determine the derivative of the given function: y = ²2t Oy=t² (2¹) + 2(2¹) (t) Oy In 2(2)…

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Q: 1. Determine the equations of the tangent and normal lines at P(1,1) given x³y - 2xy² + x² - 3y + 3…

A: To determine the equations of tangent and normal to the given curve.

Q: 4. * f(x) = x² ex

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Q: Solve the equation: loge (x + 4) + loge (x + 3) = 1

A: Given query is to find the value of the x.

Q: Consider the following. √x + √y = 3 (a) Find y' by implicit differentiation. y' = (b) Solve the…

A: See this solution in below.

Q: 6) a) Σ k=1 Determine whether each of the series below converges or diverges and explain your…

A: The given series is (k!)3/(3k)!, k from 1 to infinity.

Q: Evaluate the following integral using trigonometric substitution. S dt 1²√36-1² OC. t-6 tan 0…

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Q: (2x+3) y'= y + (2x+33 when 3. (2x+3) X x = -1, y = 0 1/2

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Q: Solve cosx dx + (sinx)y=1 Select one: O ay sinx + ccosx O b. y = 2sinx + 2cosx + c O c. y = sinx –…

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Q: 4. Find if possible, the absolute max and absolute min. for. on [0₁4 > f(x)= x X-4

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