Find the inflection points of f(x) = x¹ + 9x³ — 15x² + 15. (

Q: What region R in the xy-plane maximizes the value of (1-2x² - y²) dA? R R is the set of points (x,y)…

A: what region R in the xy-plane maximize the value of given integral.     Here i attached the solution…

Q: Consider the function below. f(x) = -2x² + 8x + 9 (a) Find the critical numbers of f. (Enter your…

A: F(x) = -2x2+8x+9

Q: If a ball is given a push so that it has an initial velocity of 7 m/s down a certain inclined plane,…

A: We have to slove above question

Q: Evaluate the iterated integral S S (11x+10y (11x+10y + 14)dx dy. 4-2

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Q: Find the value of the summation. Σ( – 3) - k 0

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Q: F) y= 4x³ In(8x)

A: y=4x3ln8xd dx(xn)=nxn-1d dx(lnx)=1xd dx(ab)=b×dadx-a×db dxb2

Q: (3) Evaluate the slope of the tangent line for the graph of the x2 x²+1 at x = 1 function h(x) =

A: The given function is: hx=x2x+1  To find the slope of the tangent line at x=1

Q: Consider the function g(t) (a) Find g '(t) = 6-1² (6+7²)² t 6 + t² (b) Find all critical points of…

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Q: For the following differential equation +4y= 1 cos (21) +71+1 di² a. Find the general solution b.…

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Q: Evaluate the double integral over the given region R SS ex- dx dy R: 0≤x≤ In (4), 0≤ys In (4) R

A: Use the common integral formula: ∫eax+bdx=1aeax+b+C   Given: ∫∫Rex-ydxdy  R: 0≤x≤ln4, 0≤y≤ln4

Q: Use the ratio test to find the radius of convergence of the power series R (If the radius is…

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Q: find the general solution of the following differential equation. y′′′ − 3y′ + 2y = 0

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Q: 2. Let a > 0 be a fixed real number. Determine whether dx xl+a [3 converges or diverges. If it…

A: Since you have posted multiple question in this question which are not interlinked so i have solved…

Q: Evaluate the integral. Answer= +C -18e² - 60 | z¥8ez +15° -dz

A: The given integral ∫-18ex-60e2x+8ex+15dx. To find the solution to the given integral.

Q: ind the Laplace Transform of the following functions, using the definition of t _aplace transform 1)…

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Q: A trough is 8 ft long and its ends have the shape of isosceles triangles that are 5 ft across at the…

A: Let b be the base of triangle and h be the height of triangle.Using the property of…

Q: Assume the functions below are continuous with domain all real numbers. (a) If f'(a) = 0, then x = a…

A: Given that:- The function is continuous with domain all real numbers

Q: A cylinder is inscribed in a right circular cone of height 7 and radius (at the base) equal to 4.…

A: I am attaching image so that you understand each and every step.

Q: An explosion sends two shards of metal to the east and to the north. The northward shard travels at…

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Q: At 1pm a bicycle is 9 ream shop travelling the ice cream shop) mpn. At the same time, another bike…

A: Given : after t hr , distance travelled by A = 15t miles  distance between A and C = 9 - 15t…

Q: aluate the limit lim x→1 ƒ(x)-ƒ(1) x-1 using the limit toolkit developed in class

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Q: Determine whether Rolle's Theorem can be applied to f on the closed interval [a, b]. (Select all…

A: To find out that Rolle's Theorem can be applied to f on the given closed interval or not.

Q: f(x) = cos² X-T 2 ; g(x) = sin(x) +ln(cos(x)); k(x) = cos(√x - √e) ln(√x - e); h(x) =…

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Q: Use row reduction to find the inverse of the given matrix if it exists, and check your answer by…

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Q: A tank with a rectangular base and rectangular sides is open at the top. It is to be constructed so…

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Q: 8. A bead slides down the curve xy = 10. Find the bead's horizontal velocity at time t = 2 s if the…

A: given  xy=10geight, y=400-16t2horizontal velocity=dxdtd dx(xn)=nxn-1d dx(a.b)=adbdx+bdadxd…

Q: (d) 4x²y" + y = 0, (e) y" + 16y = 0, Y₁ = √√x ln x Yı Y₁ = cos(4x)

A: see below the answer and calculation

Q: Consider the function g(x) = x³ - 12x. (a) Indicate the x- and y-intercepts. (Order your answers…

A: We are authorized to answer three subparts, so we answering the first three subparts.

Q: Find the following limit. lim V

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Q: Solve the equation y' - y=f(t), y(0) = 0 0 1 Be sure to supply all the steps that leads to your…

A: The solution is shown below-

Q: Concentration of a Drug in the Bloodstream The concentration (in milligrams per milliliter) of a…

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Q: Let a = 1 and b = 4. 0 16 S.L. ㅠ -√a²-x² If you need to use π for your answer, just type pi.…

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Q: The graphs of the functions, f, g, and h are shown below. Each function is NOT differentiable at x…

A: The solution is shown below-

Q: In a trend that scientists attribute, at least in part, to global warming, a certain floating cap of…

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Q: (5) If y = sin(3x) the find y"

A: We have given trigonometric equation  y=sin3x y'=dydx y'=ddxsin3x y'=cos3x·ddx3x y'=3cos3x…

Q: Verify that the given differential equation is exact; then solve it. (21x²y³ + 4y) dx + (21x³y² + 4y…

A: As per our guidelines we are supposed to answer only one question. Kindly repost other question as a…

Q: Find the distance between the skew lines: z=8-9t x = 5+7t, y=3+7t, x = 1-t, y = 6, z = 5+8t NOTE:…

A: Solution:  To find the distance between the following skew lines. x=5+7t, y=3+7t,  z=8-9tx=1-t, y=6,…

Q: 14. Solve the initial value problem du = ² + 1 with y(0) dy = 1. dt Oy(t) = Oy(t) = t³+t-1 Oy(t) =…

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Q: Find an equation of the plane with the given characteristics. The plane passes through (0, 0, 0),…

A: As we know that, To expression to calculate the equation of the plane when it passes through the…

Q: Write out the form of the partial fraction decomposition of the function: - Sº A Determine the…

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Q: Find parametric equations for the line whose vector equation is given. (a) (x, y) = (4, -6) +…

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Q: Part 1 Differentiate f(x) Answer: Part 2 df dx f'(x) = x³ - 4x + 5 x3 If f(x)=√x sinx, find f'(x).

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

Q: Let f(x) = x(x-4)³. (a) Find the critical number(s) of f. (b) Find the interval(s) on which f is…

A: (a) A critical point is a point of a function where the gradient is zero or not defined (the…

Q: A function y = g(x) has a derivative shown below for -3 ≤ x ≤ 3. Three -3 O Four 312 3 (b) Where is…

A: Answer: The solution is given below:

Q: For each function a) find the critical points/numbers, b) intervals of increasing/decreasing c)…

A: Given function:- fx=3x2-4x+6

Q: Find the cross product a x b. a =j+ 6k, b = 2i -j + 5k Verify that it is orthogonal to both a and b.…

A: The given vectors are: a=j+6k, b=2i-j+5k

Q: The general solution to the differential equation. expression for f (x) and its domain? A (В C D…

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Q: Suppose that f is a function given as f(x) = -3x² - 2x - 3. Simplify the expression f(x + h). f(x +…

A: f(x)=-3x2-2x-3(i) f(x+h)=-3(x+h)2-2(x+h)-3

Q: for the following question above help me solve f

A: Given : for x<-1f'(x) = ddx(-x+1)=-1for x>-1f'(x)=ddx(-x2+3)=-2x

Q: 1) Find the radius of convergence for f(x) =(-1)^4+1 ²n+1 n=0 4n+2

A: