In how many ways can 8 campers sit around a campfire? 5,040 5,760 40,320

Q: 2. a) Calculate the 4th roots of (5 - j3) b) Differentiate the following functions clearly showing…

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Q: EC) Determine the value of the definite integral -1 ² (4x³ + 5)³dx .

A: The given definite integral,     ∫-10x24x3+53dx

Q: Let f(x) be a function given by f(x) = (a) Prove whether f(x) is a Dirichlet function. (b) Find the…

A: Given

Q: B. For the figure shown below, find the sum of the areas of all the semicircles. 47

A: I am attaching image so that you understand each and every step. Answer is 227π512 square unit

Q: Determine the equation of the ellipse with foci (1, 4) and (-5, 4), and co-vertices (-2,8) and…

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Q: y 3. The region bounded by the curve y=sec x, the x axis, the axis and the line x=0.25pi is revolved…

A: The given curves are; y=secx, y=0 x-axis, x=0 y-axis, x=0.25π So, the bounded region is as shown…

Q: Evaluate the following: 1. f(x³ + 3x²)dx

A: Since you have asked multiple question, we will solve the first question for you as per our guide…

Q: Convert the following parametric curve into Cartesian form: x=2 sint, y = 3 sin t O 3x² + 2y² = 1 O²…

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Q: Evaluate the integral. (Use C for the constant of integration.) ] = 5 tan(x) sec³(x) dx

A: The given integration is: ∫5tanxsec3xdx To find the value of integration.

Q: Find the transition points. y = 2x6 - 18x4 (Use symbolic notation and fractions where needed. Give…

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Q: (b) Show that the interval of convergence of the series n=1 sest 2-12-1 (4n-3)² is given by

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Q: Evaluate the following integrals: dx dx ·S b. S √81+16x² √16x²-9 a. dx 49-4x² c. S.

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Q: S # 3 X Use the fundamental Identities to simply the expression. 1) tan & coft 2) cos²0 2 +CSCO sint…

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Q: tid Q3. Evaluate the following integrals 1) cothx.csch2x. dx (50-3x - √x+1+73 44x

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Q: Determine whether the series is convergent / divergent (4) Σ.Ξ1 +∞ 1

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Q: b) Calculate the following integrals x²(3x³ + 2)²dx (i) (ii) sin3x e³x dx (ii) (2x22+₁ +*²+2) dx S…

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Q: 5. The Fourier transform of signal e²²¹ u(t-3) is . e-3(2-jw) a) 2-jw b) e-3(2+jw) 2+ jw c) e3(2-jw)…

A: NOTE: As per our guidelines, I have solved one question. If you want the answers of rest, kindly…

Q: 4. Find the slope of the tangent to y = sin² (2x) at x = 12

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Q: Find the area of the region between the graphs of y = 16-2² and y=-62 +9 over the interval -3 ≤z≤1.…

A: Given: y=16−x2 and y=−6x+9 Let's first find the intersection point of y=16−x2 and y=−6x+9 16-x2…

Q: If r(t) = (3t, 2t², 4t³), find r'(t), T(1), r"(t), and r'(t) x r"(t). r' (t) = T(1) = r"(t) = r'(t)…

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Q: A balloon is rising at a rate of 3 meters per second from a point on the ground 55 meters from an…

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Q: (5) Σ.1 η=1 η! 102n-1

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Q: 2. Evaluate x sin ædr using integration by parts.

A: Given: I=∫xsinxdx   We know the basic integration formula. ∫sinxdx=-cosx+C∫cosxdx=sinx+C

Q: f (x) = 2x+7 if -5=Xcl 8 If X = 1 14X=3 if 11x-2 31 If x > 3 IS this continuous at X=1 ? formula…

A: Any function f(x) is continuous at x=a if  lim x -> a f(x) = f(a) i.e. Functional value at that…

Q: 4.) Find an equation for the plane tangent to the surface 9x² +4y² +9z² = 34 at the point (1,2,-1).

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Q: 62-24 x²+2x-8 5. Analyze the function from its equation y determine the non-permissible value(s) the…

A: The non-permissible value of a rational functions are obtained by equating the denominator to zero.

Q: drug is administrated intravenously of the object iver 1. the time interval [3,8] Use definition of…

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Q: Suppose F(4)=-4, f(x)cos F(x) dz F(5)= 3, and F'(x) = f(x). 3 cos (3) +4 cos(4)

A: We can evaluate the given integral by using the substitution u= F(x).

Q: Numerical Integration: 1 So Fede dx 1. 0 2. 2 (2x² – 3x) dx -

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Q: For the function f(x) (X^2-3 if -3 ≤x2 C) is f continuous at x=2? D) does lim f(x) exist at x->4^-?…

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Q: Let f(x, y) = 2x and C be the line segment on the plane from (0, 0) to (3, 4). Evaluate the line…

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Q: QUESTION: 2. Sketch the graph and solve for the volume of the solid generated by revolving along the…

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Q: ·Sa 20. x² dx (x − 1)(x² + 2x + 1)

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Q: Evaluate the following limits: 2. lim G(x) if G(x) = = x →-00 x+61 x+6 2

A: We have to find the limit

Q: Suppose that f(x, y) = y√√³+1 on the domain D = {(1, y) | 0 ≤ y ≤z≤ 4}. Q Then the double integral…

A: NOTE: Refresh your page if you can't see any equations. . here we have

Q: Find the exact coordinates of the centroid for the region bounded by the curves y = 4-2² and y = 0.…

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Q: n 2sin(x)=1, on the interval 10, 2π], what is the value of x?

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

Q: Fill in the blanks to describe the transformations that occur in the the graph from the Parent…

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Q: Let F(x) = x √ √2+1 dt. Find F"(1) 3

A: Given: F(x)=∫3x t2+1dt Leibniz integral rule for differentiation states that ddx∫a(x)b(x)…

Q: In APQR, p = 6.7 inches, r = 2 inches and /R=142°. Find all possible values of ZP, to the nearest…

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Q: The function f(x) = 3x ln(1 + x) is represented as a power series f(x) = Σ cnon n=0 Find the…

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Q: =iven √x³√4-x² dx. If we letz= √√4-x², which of the following integrals is correct using…

A: We have to substitute z=√(4-x^2)

Q: y = 2 sin (20+ 4π 3 ^

A: Given query is to find phase shift.

Q: Find the average value of f(t) = -2te Answer: -0.63 on the interval [0, 1].

A: topic- average value of function over interval

Q: If 2 = (6,-5) and a = (-2,6), find |2+3.5d |. O 5√11 O √146 O 16 2√73

A: topic- vectors

Q: 10) Using the First Derivative Test, what are the local extrema for the function 5(x)==x²+10 x³…

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Q: Solve - cos2 - sin²x = 1 on the interval 0 < x < 2T. O 3π 2' 2 O no solution O 0, T O 0, T, 2T

A: The given equation,    -cos2x-sin2x=1 on the interval 0≤x≤2π

Q: The graphs of a quadratic function and a cubic function are shown below. Both graphs have integral…

A: Given problem:-

Q: mph. Ship A leaves port sailing west at a speed of 30 mph. Six hours later, Ship B leaves the same…

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Q: y = lnx and x-y-4 = 0

A: