["(x² (x² + 8)e-x dx

Q: 7) Find the relative extrema of the function f(x)=sin² x+sinx in the interval [0,2π].

A: The first derivative test is based on the sign that the first derivative is around the point that we…

Q: Question Find the equation of the tangent line at the point (1, -3) to the curve defined implicitly…

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Q: The acceleration of an object (in m/s²) is given by the function a(t) = 6 sin(t). The initial…

A: The acceleration of an object (in m/s2) is given by the function .The initial velocity of the object…

Q: Find the area represented by the definite integral. 13 0 kx- |x-10| dx

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Q: 57 Find the four second-order partial derivatives for f(x, y) = 7x³y² + 8xªyº. fxx² ¹ w=0 fxy=0 fyx

A: Given,Finding the first derivative for the given equation:Differentiating the given equation…

Q: Current Attempt in Progress Evaluate the integral using an appropriate substitution. NOTE: Enter the…

A: The given integral is x3+5)3

Q: Over which interval of a values is f'> 0? THE FREATES 10000 DE TO PREORDED 1232528287 OSTALBOTER…

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Q: Use appropriate algebra and Theorem 7.2.1 to find the given inverse Laplace transform. (Write your…

A: To find the inverse Laplace transform.

Q: 5. Find the area of the shaded section for the limacon r = 2 cos 0-1 D 2 -X

A: We need to find area of the limacon.

Q: Consider the surface with parametric equations r(s, t) = (st, s+t, s-t) A) Find the equation of the…

A: r(s,t)=

Q: For the following function, determine whether the function is one-to-one. {(2,9), (5,9), (-9,14),…

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Q: Analyze the equation. That is, find the center, vertices, and foci of the ellipse and graph it. 2 2…

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Q: The graph of function f (x) is shown below. At which value of x is the slope of the tangent line to…

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Q: Let / be a function defined for t≥ 0. Then the integral (RD)) = f* e-str(t) dt е is said to be the…

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Q: Evaluate. (Be sure to check by differentiating!) √(6+x¹)x³ dx [(6+x²) *xx X (Type an exact answer.…

A: The given integral .We have to find the integral.

Q: the series converges conditionally, converges absolutely, or diverges. gent vergent

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Q: 12) Find the area of the region bounded by the curves y=x² - 4x+3 and y=-x²+2x+3.

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Q: Find the slant asymptote of y x² + 4x + 5 x + 4

A: y=−x2+4x+5x+4

Q: Find the volume of the region bounded above by the elliptical paraboloid z = 7 - 3x² - 2y² and below…

A: Region bounded above by the elliptical paraboloid z=7−3x2−2y2and below by the rectangle…

Q: 2. Suppose a particle is traveling on a one-dimensional track with velocity v(t) = t² - 6t+ 5 feet…

A: Given: To Find:(a) To find the position function.(b) To find the acceleration function.(c) To find…

Q: 1 Let R be the region in the first quadrant below the curve y Compute the volume of the solid…

A: Region is bounded by y=11+x2 from x=0 to x=1.Rotating the region about y−axis.Using the shell method

Q: Degree: 4 ; zeros: 2i and -5i Form a polynomial f(x) with real coefficients

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Q: Find the indefinite integral. (Use C for the constant of integration.) /(- 800 (0.04p - 1)3) Now…

A: To solve:

Q: elf" (x) Find the maximum value of f(x)=√1+x² [0,2] on the indicated interval.

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Q: Question What is the first derivative of h(x) = = 4(x³) ? Provide your answer below: h'(x)= =

A: Here we have given a function h(x).

Q: 1 Suppose that f is a function given as f(x) = −3x – 1 We will compute the derivative of fat x = 7…

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Q: = p'(x) if p(x) = In 5x2+x+6 x 5 tan x

A: p(x)=ln⁡(5x2+x+6x3/5tan⁡x)Using logarithm propertiesloga⁡(mn)=loga⁡m−loga⁡nloga⁡(mn)=loga⁡m+loga⁡n

Q: B ed a A σ Use the right triangle and the given information to solve the triangle. a=2, c=6; find b,…

A:

Q: Express the Cartesian coordinates (1,-1) in polar coordinates in at least two different ways. Write…

A: The given cartesian coordinates is .The aim is to find the polar coordinate in two different ways.

Q: Sketch a graph of the pair of parametric equations. Mark the direction of the graph by using small…

A: Consider the equations

Q: Given the differential equation: D(D³ + 2D² + 10D)y = 0. What are the roots of the auxiliary…

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Q: Question Determine f'(x) if f(x) = x¹0 arcsec(x). Provide your answer below: f'(x) = [

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Q: Find g'(1) if g(x)=6x³-6x² Og'(1)=8+√6 Og'(1) = 8 g'(1)=14+ √6 Og'(1) = 14 +√6. +8x+-

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Q: Evaluate the integral below by interpreting it in terms of areas. In other words, draw a picture of…

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Q: Use partial fractions to find the power series of the function: 18 n=0 x +42 (x − 2)(x + 9)

A: The given function .The aim is to find the power series of the function.

Q: Find the height of the tower using the information given in the illustration. The height of the…

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Q: Jose invests $200 in an account with 5% APR compounded monthly. (a) Give the formula for the amount…

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Q: 5. For a particular pain medication, the size of the dose, D, depends on the weight of the patier W.…

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Q: Find the following for the vectors v = 11i +2j-10k and u = 5i + 12j. a. v•u, |v|, |u| b. the cosine…

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Q: T 12.Given h(x)=xinx find the equation of the tangent line at x == 2

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Q: Question 10 of 10 < Which constant c would best be described as a constant of integration? ° [ f'…

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Q: Find a number a in [0, 1] such that f(a) = fave over the interval [0, 1]: f(x) = 3x² 0 √3 3 1 √3 3

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Q: The function f is one-to-one. Find its inverse 8 f(x) = 6 x 6 X-6

A: f(x)=8x−6,x≠6

Q: . For example, if Eloisa invests in an I-bond which compounds twice a year with APR 8%, 8% then each…

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Q: Use the form of the definition of the integral to evaluate S L.² (₁. (4 - 2x) dx the properties of…

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Q: A company has the linear total cost function C(x) = 22x + 2109. (a) What is the company's marginal…

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Q: (2x-5)" Find the radius of convergence R and the interval of convergence I of the series 1 3 n³…

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Q: 19) Besides y=-x³, pick at least 2 other functions with odd exponents to explore. List in the…

A: According to our guidelines, we can answer only first question (due to multiple questions). Kindly…

Q: The functions f(t) and g(t) are shown below. ---110 |--1 1,0 (a) The slope of the graph at (0.25,…

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Q: Consider the parametric equations below. x = t2 − 2,    y = t + 3,    −3 ≤ t ≤ 3   Eliminate the…

A: Given,