1 Consider the function f(x) : 2x. At what value of T does f(x) 48 have a critical point? Round your answer to 2 decimal places

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A: We have to solve above question

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Q: H.W: which series converge and which diverge, and if a series converge find its sum: 1. E(zr n+1 3…

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Q: 2.4

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Q: 20 . Using the definition of derivative at a point, f'(9) f(x) – f(9) x – 9 Let f(x) lim enter %3D…

A: Given: fx=20x It is given that definition of derivative at a point x =9 is defined as…

Q: АВ C D E F This is a graph of f'(x), the derivative of f(x)

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Q: Find the arc length of the parametric curve. = 4 cos(t), y = 4 sin(t), z = 3t; 0<t<T %3D

A: Use arc length formula

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A: We will find if this is exponential.

Q: Evaluate the definite integral. NOTE: Enter the exact answer. ti +t°j dt 0.

A: this is a problem related to vector integration. Based on the general formula and concepts we will…

Q: Use the ratio test for absolute convergence to determine whether the series converges or diverges.…

A: The idea of ratio test must be there to understand it properly. The explanation part is given below.

Q: Find the limit. NOTE: Enter the answer using round brackets. t2 +9 1 lim tto 9t2 + 10' 7t |(?,?)

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Q: if x 2 valuate each of the following, if it exists. (If an answer does not exist, enter DNE.) lim…

A: Solution of given question is written in below steps.

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Q: Determine the real values of a, b, and c for the quadratic function Ax) = ax + bx+c, a +0 that…

A: Here we have to determine the real values of a, b, and c for the quadratic function f(x)=ax2+bx+c…

Q: How much work is required to pump all the water from a right circular cylindrical tank, that is 8…

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Q: Find T(t) and N(t) at the given point. x = e' cos t, y = e' sin t, z = e'; t= 0 T(0) : N(0) =

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Q: me origin is 6i + 8j, then the me direction of a = 3i + 4j at

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Q: 4. S(e* + vx – x* + 2)dx = %D

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Q: Evaluate both integrals of the Divergence Theorem for the following vector field and region. Check…

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Q: Evaluate (2x - y) dx + (x + 3y) dy. C: arc on y = x/2 from (0, 0) to (4, 8)

A: Here we have to evaluate        ∫c (2x-y)dx+(x+3y)dy

Q: MP USING TOOLS Use a fraction or a mixed number to represent the tiT on a number line. Let 0…

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Q: The integral of the given function csc °x dx is equal to 3cos x-10stn²x cos>x-15sin"xcosx + C…

A: I=∫ csc6x dx =∫ (cot2x+1)2 csc2x dxu=cot xdu=-csc2x dx=∫ -(u2+1)2 du      =∫(-u4-2u2-1) du…

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A: Given problem:-

Q: Use Green's Theorem to evaluate the integral (2x? – y)dx + 4xdy where C is the circle x? + y² = 9…

A: To evaluate the given integral using green's Theorem.

Q: If a person learns y items in æ hours, as given by y = 19V2?, find the rate of learning for a person…

A: We need to find the rate of learning.

Q: ergence Theorem to find the flux of F(x, y, z) = (x - z)i+ (y – x)j+ (z – urface of the cylindrical…

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Q: Use Green's Theorem to evaluate the line integral. Iy? dx + xy C: boundary of the region lying…

A: A detailed solution is given below

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Q: A stone is dropped into a lake, creating a circular ripple that travels outward at a speed of 50…

A: The speed of ripple that travels outward = 50 cm/s

Q: 2. Write the given (total) area as an integral. a. The area above the x - axis and below y = 4 – x²…

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Q: uppose that F(x, y, z) = 0 defines z as a function of x and y and F is differentiable. "rove that dy…

A: Given F(x,y,z)=0

Q: Suppose the total revenue function is 4x? + 3x + 2. Find the average and marginal revenue. In…

A: Note:  In question 3, the function given is incorrect. So, i am solving the question 4. Question - 4…

Q: Determine the integral of sec^4 (x) tan^2 (x) dx * O 1/7 sec^7 (x) - 1/5 sec^5 (x) + C 1/3 tan^3 (x)…

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Q: A rectangle is inscribed with its base on the x- axis and its upper corners on the parabola y = 8 –…

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Q: aph the function g(x) = x* + 2, if x < 1 Is the function continuous? Explain. x +2, if x 2 1

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Q: Find an equation for the tangent line to the curve parametrized by x = 4t y = est at the point t =…

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Q: The half-life of a radioactive substance is 11 days. After 3 days a sample of the substance has been…

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Q: Confirm that the force field F(, y) = 2xy°i + 3x²y°j is conservative in some open connected region…

A: If force field is conservative then it is independent of path.

Q: 2. Consider points O(0, 0, 0) and A(0, 0, 3). Show that the set of all points P such that 2|OP| =…

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Q: The Trapezoidal Rule ou e id b oblw Jeot en f (x) dx = h +f(x1) + f(x2) + ..+ f(xn-1) +f(xn)) b-a…

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Q: )4 Evaluate (nx) dx

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Q: In the given integral below, what is the values of u and a? * dx УЗ — х2 — 2х и 3 х+1аnd a — 2 и 3…

A: This question is based on indefinite integral.

Q: 1. A line, passing through point (6, 3, 2) and is perpendicular to the yz-plane. Find a point on…

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Q: Describe the graph of the equation. r = 5 sin 14ti + 5 cos 14t j O It is a circle of radius 14 in…

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Q: Use the method of cylindrical shells to find the volume V generated by rotating the region bounded…

A: Find your answer below

Q: Using any method, find the value of F. dr if F(x, y) = (8e" + 2ye")i+ (2e" + 8xe") j and nt C:r(t) =…

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Q: Differentiate h(t) = 54ª %3D

A: Solution of given question is written in below steps.

Q: Consider the curve defined parametrically by x(t) = cos(t), y(t) = sin(t), te [0, π] (a) For what…

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