I. Evaluate the following integrals. •ln 2 #3. e2" sec-(e")dx

Q: Find the most general antiderivative of the function. (Check your answer by differentiation. Use C…

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Q: [ 3x3-2х2-4х-3 х2 (х2+x+1)

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Q: 4. Find the average value of the function over [1,4] and all values of x in this interval for which…

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Q: Find the directional derivative of the function at P in the direction of v. f(x, y, z) = xy + yz +…

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Q: (x² + 2x) cos(2x) dx

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Q: x* Find the exact length of the curve y =- 1 2<x<4.Show All Work and Give Answer In Simplest Form.…

A: We have to find length of a curve for the given interval.

Q: What is the appropriate substitution to solve dy/dx + ln(x+1)y/x = x^3y^3? z=y^-2 z=y^2 z=y^3 y=vx

A: I am going to solve the given problem by using some simple calculus to get the required result of…

Q: +00 (5 – 4(ln n)*)" Σ (V3. In n)3n n=2

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Q: x- 2 7) dx =

A: integration

Q: A true statement for the function f(x)=2x³-3x²+10 is.... Pernyataan yang benar dibawah ini untuk…

A: The given function is: f(x)=2x3-3x2+10 Now, f'(x)=2(3x2)-3(2x)=6x2-6x=6x(x-1)

Q: Solve the equation 6cos?x + 11cos x = -4 given that 0 < x < 2n. Provide your answer below: X =

A: First I have made factor of given trigonometrical equation and then seperetly solved them and find…

Q: A particle moves along the x-axis with velocity given by v(t) = 3t2 + 12t – 6 for timet > 0. If the…

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Q: Determine whether the following series converges or diverges. If the series converges, determine the…

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Q: Find the sum of the convergent series below. Show complete solution

A: This question is related to infinite series, we will solve it using given information.

Q: Evaluate: - / (e* -e*)dx e ¯X+C 2 A | B) None cosh x +C 1 - sinh x +C 2 D E sinh x +C F -cosh x + C…

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Q: Let (x* + 5)' a Let [(x* +5) x*dx = 12116. Then the value of a is ...

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Q: Find the sum of the given convergent series. > [tan-1(2n – 1) – tan-1(2n + 3)] n=0

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Q: bx2 ) e x2c +d X. dx

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Q: Show that the equation has exactly one real root. x° + e* = 0 3

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Q: Exv3x² + 4 dx %3D 1 (3x² + 4)v3x² + 4 +c 3

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Q: Determine the third degree Maclaurin polynomial of f(x) = tan 3x. Use this to approximate the…

A: We need to find approximation by using Maclaurin series.

Q: Solve the given initial-value problem. dx x = 6y2, x(9) = 1 y - dy x(y) = Give the largest interval…

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Q: The acceleration function (in m/s?) and the initial velocity are given for a particle moving along a…

A: We have to find value of v(t) and x(t)

Q: Use the first derivative test to find the location of all local extrema in the interval (0, 27) for…

A: answer is in  next step

Q: I. Evaluate the following integrals. Зx3—2х2-4х-3 dx x² (x²+x+1) 2.

A: Given: I=∫3x3-2x2-4x-3x2x2+x+1dx   As we know that; The Power rule: ∫xndx=xn+1n+1+C ; n≠-1 And…

Q: 570 8. The demand function of an electronics company’s car stereo is p(x) = 2х +7 Find the consumer…

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Q: Preview Activity 1.4.1. Consider the function f(x) = 4x - x². a. Use the limit definition to compute…

A: This question can be solved using the concept of limit definition of derivatives.

Q: Va2 – 4 dx

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Q: dx b. (x² + 1)(x² – 2x + 1) -

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Q: The round off errors when measuring the distance that a long jumper has jumped is uniformly…

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Q: A particle moves along the x-axis with velocity given by v(t) = 6t2 at time t = 0, what is the…

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Q: 1. Evaluate the following integrals. (a) r* log r dr

A: Since the student has posted multiple questions and does not mention any specific question, so we…

Q: Find the third degree Maclaurin polynomial for f(x) = cot-1(x) and use this to approximate…

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Q: Let A = (1,0, 2) and B = (6,-2,3). Solve for projĄB.

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Q: The tangent line equation of x4+y=32 at point (2,-2) is...

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Q: Evaluate: y6 sech(e™ny) tanh (e 7Iny)dy (A sech (y") + C -sech2(y7) + C 7 В -uch(7") + C (y?) +C D…

A: Given: I=∫y6seche7lnytanhe7lnydy   As we know from the logarithmic rule: (1). logaxb=b·logax, x≥0…

Q: Use sigma notation to write the sum. 1 +. +. 9(1) 9(2) 9(3) 9(11) 11 Σ i = 1

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Q: -1x) dx

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Q: Solve the system of equations by any method.   −4x+8y    =28 x−2y    =−7   Enter the exact…

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Q: Q2) Solve the D.E xdy + (2y – xª + 3x)dx = 0

A: This is a problem related to differential equation. Based on the general formula we will answer the…

Q: f(x) dx = | IS(x)| dx =

A: Integration is the area under the curve and x-axis.

Q: Use the method of Lagrange multipliers to find the points on the circle x2 + y2 = 52 that are…

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Q: An irrigation sprinkler in a field of lettuce sprays water over a distance of 25 feet as it rotates…

A: We are going to slove above question and find the area of field

Q: y = log v2x + 5

A: i have provided this answer with full description in step-2.

Q: - Evaluate the following integrals. 1 1. J x(9 – In² x}5/2 dx

A: To evaluate: ∫1x9-ln2x52dx Let, I = ∫1x9-ln2x52dx

Q: 3. 6x° cos (x*) dx

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Q: 6. lim e (x, y)→(1, –1) cos(x + y) -xy

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Q: Use trigonometric substitution if possible dx x? (9x2 – 4)2

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Q: dy Find dz and simplify: y = ln(2x + V1 + 2a²)

A: The objective of the question is evaluate the derivative of the given function.

Q: 7. Find the area of the region that lies inside the curve r = 3cos0 and outside r = 1+ cos0. Show…

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