Determine the resulting definite integral after making the following substitution: • ¹/3 So 1 4+9x² dx where u=3x

Q: K Find the indefinite integral √(-2 -2 sec x tan x +5 sec x +5 sec² x) dx = -2 sec x tan x +5 x) dx.

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Q: The parametric equations and parameter intervals for the motion of a particle in the xy-plane are…

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A: f(x)=x3/8, a=16

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A: .

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Q: Consider the following function. 1 (x-4)² Step 1 of 2: Determine the more basic function that has…

A: The given function is,

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Q: Sketch the curve with the polar equation r = 2 + 2 cos(0). What is the name for the shape of the…

A: Given that the polar equation

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A: The differential equation is given byThe auxiliary equation corresponds to the differential equation…

Q: Problem #7: Evaluate the surface integral f FdS where F(x, y, z) = xyi - y²j-9zk and S is the sphere…

A: Calculate F.dS where  F(x, y, z)  =  xyi − y2 j − 9zk  and  S is the sphere  x2 + y2 + z2  =  9…

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A:

Q: Let u = (5,-4) and v= (-4,7). Find the (a) component form and (b) magnitude (length) of the vector.…

A: The vectors are given by(a) The component form of the vector  can be obtained as follows:

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A: jane is 2mi offshore in a boat and wishes to reach a coastal village 6mi down a straight shoreline…

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A:

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A: The width of each sub interval is ( 9π/8 - π/8 )/4 = π/4We can calculate the height of each…

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A: The graph of the function  is given as,Estimate the slope of the tangent line to the curve at

Q: (i) Find the derivative of the function. esin x COS X In(1+2v) dv.

A: To find the derivative of the following function.

Q: The hull speed (in knotts) of any watercraft is given by V = 1.34-L¹/2 where L is the length of the…

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Q: For Evaluate the following expression. Select the correct answer below: f(x) 4-x-x² ifxsl 2x-1 ifx>1…

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Q: *P(zx) ulg*J

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Q: Suppose k(x) = f(g(h(x))). Given the table of values below, determine k'(-2). f(x) g(x) h(x) f'(x)…

A: xf(x)g(x)h(x)f′(x)g′(x)h′(x)−2−4−1046−7062−11−3820−5−8237

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A: The given roots of equation are

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Q: Find the area of the region between the curves y = x(1-x) and y = 4 from x=0 to x = 1.

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Q: 9. Suppose 0 < a <b, and Find the value of få f(x²)dx. A. 4 B. 2 C. 1 D. -5 [F(x²)dx=6₁ ["f(x²)dx =…

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Q: A cell culture contains 4 thousand cells, and is growing at a rate of r(t) thousand cells per hour.…

A: Substitute t=5 in r(t) and solve, an then add 4 thousand to it.

Q: Evaluate the line integral e F. dr where F H ScF. dr = (5 sin x, 5 cos y, 5xz) and C is the path…

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Q: Find the domain of the function. 5x x²-4 X g(x) =

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Q: T In the closed interval 0≤x≤3, if h(x) = k·cos -x, for what value of k does the region bounded by…

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Q: F(x) F(2) (5) F(7) - L² (t³ + 6 t F(x)= (t³ + 6t-5) dt

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Q: Evaluate the following indefinite and definite integrals using substitution.  Show all work, thank…

A: use substitution method for solving such integral

Q: ηλη Σ (2η)! n=1

A: The given series .The aim is to determine whether the given series is converges or diverges.Ratio…

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Q: Which of the functions shown below is differentiable at x = 0? Select the correct answer below: -

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A: Firstly find inflection point (f"(x)=0).Concave upward: f"(x)&gt;0.Concave downward: f"(x)&lt;0.

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Q: Find the Cartesian coordinates of the following points (given in polar coordinates). a. (1,0) b.…

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Q: Find y'' if y=-8 cos x. OA. y'=8 sin x OB. y'= -8 cos x OC. y'= 8 cos x OD. y'= -8 sin x

A: Explaination of answer is as follows

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Q: Evaluate the improper integral O a.-2 O b. 1 042 C 3 X

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Q: 1 A 3 2 1 a 1 To find the blue shaded area above, we would calcula b f(x) dx = area Where: a = 1…

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Q: Which of the following is the correct result of 07 15 02 O 15 2016 -I +C 5 H wj* 05 1 21 :+C +0 of […

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Q: Match the graph of the function on the left with the derivative on the r 1. a. 2. 3. 4. -10 10 -10…

A: Note:-Since you asked multiple sub parts questions, according to our policy we can solve only first…

Q: Find the domain of the function. f(x) = -5x + 3

A: f(x)=-5x+3

Q: (b) log321 +2/og33 Answer: log3 189 ! No, that's only partially correct

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Q: For Questions 1 and 2, region R is bounded by f(y) = y²- 14 and g (y) = 2y +1. Which of the…

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Q: Find a, b, c, and d such that the curve ?=??3+??2+??+? has its tangent line at(1, 1) and at (0, -2)…

A: The objective of this question is to find the coefficients a, b, c, and d of the cubic function y =…