7. g(x) = In (3V4 + x² ) %3D

Q: Use series to estimate the lim m X-1

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Q: 4.) Evaluate: xe* dx

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

Q: Ballast Dropped from a Balloon A ballast is dropped from a stationary hot-air balloon that is…

A: Given query is to find the height of the blast after t time and the time when it will hit the…

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Q: 2.7 Given the function f(x) = r²e, Determine the open interval(s) where the functio

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Q: 1 liter of paint that costs 200.00 pesos can cover 13.33 square meters, exactly how much will be…

A: This question can be solved using the concept of units and measurement.

Q: Find exactly T() and N() for x- e'cost, y = e'sint, 2- e' for : - 0. [Choose the correct answer.)…

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Q: 10. f(x) = x² + x + %3D 1 x2

A: Derivate both side with respect to x

Q: Let F(x) = f(x*) and G(x) = (f(x))* . You also know that a? 5, f(a) = 3, f'(a) = 3, f'(a*) = 9 %3D…

A: Given that,F(x)=fx3 and Gx=fx3

Q: Find the Indefinite Integral using the substitution x 7 sec(0). (Use C for the constant of…

A: Solving

Q: 52.8706e-0.3277t h'(t) - (1 + 2.449e-0.327M;2 hes/year, where the child's height h(t) is measured in…

A: Given :

Q: 3. Find the derivative of each of the following functions. Justify your answer. I sin z (a) f(x) =…

A: As we know that; The Product rule: f·g'=f'·g+f·g' The Chain rule: fgx'=f'gx·g'x   And…

Q: 03 Evaluate J (3-2x)5 using substitution

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Q: Find the derivative. dx dx

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Q: In calm waters, the oil spilling from the ruptured hull of a grounded tanker forms an oil slick that…

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Q: Differentiate 1)2xsin-13x x+1 2)y = In; Vx-2

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Q: Consider the integral / 3x* (25 + 1) dz. In the following, we will evaluate the integral using two…

A: ∫ 3x4x5+1dx=3·∫ x4x5+1dx=3·∫ x9+x4dx=3∫ x9dx+∫ x4dx=3x1010+x55Add a constant to the…

Q: 7) A rectangle has its two lower corners on the x-axis and its two upper corners on the curve…

A: Follow the procedure given below.

Q: 12. The function f(x) and its first and second derivatives are as given below. f(z) - 2 6- 2z g"(z)…

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Q: dy The curve with equation y = 1-x has a stationary point in the interval -1 <x < 1. Find and dx…

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Q: Find the derivative of the given function. dx %3D

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Q: Find the derivative w = sin* y cos*y a. sin³ 2y cos 2y b. sin² 2y cos 2y c.sin 2y cos 2y d. sin 2y…

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Q: 2 4 - 8 Q - The determents|A| of matrix A =-1 - 3 6 is 7 - 2 c) -20 5 d) none of them a) -24 b)-32

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Q: When evaluating the following integral 16dr using trigonometric substitution, Part A The correct…

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Q: The radius of a circle is to be measured and its area computed. The error in the measurement of the…

A: Since you have asked multiple questions in a single request, we would be answering only the first…

Q: Let g(x) = (t)dt, where f is the function whose graph %3D AY 21 1.5 1 0.5 0,5 1 -0.5 -1 a. At what…

A: Graph of function

Q: Evaluate: * dx re+1 5.) X-

A: Find your answer below

Q: In the following diagram, the rectangle ACEG is divided into four congruent rectangles. F E a) List…

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Q: Find the 11th term of the arithmetic sequence. $1264.02, $1946.38, $2628.74, ... a11 = $ (Type an…

A: This is a problem of arithmetic series. Please follow the procedure given below.

Q: Q2\Find the point at which the tangent to the curve y = v4x2 + 1-2 has its slop 2

A: Given: y=4x2+1-2 Slope = 2 We know that slope of tangent to a curve y is defined as dydx

Q: / (22* + 3,/5 +) Calculate the indefinite integral: dz

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Q: ab³/2 (7) If x = then log(x) = c2d' %3D (A) log(a) + log(b) - 2log(c) - log(d) (B) log(a) + log(b) -…

A: Given problem:-

Q: Let y = tan(3x + 6). Find the differential dy when x = 2 and dæ 0.2 Find the differential dy when x…

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Q: Find the limit. Use l'Hospital's Rule where appropriate. If there is a more elementary method,…

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Q: Show that the following functions satisfy Laplace's equation 0. dy? %3D (a) f(r, y) = r*y – xy³

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Q: šin(3x) Find the area bounded by the curve y = ,0 <x<T/3 and the line y = 0 as shown 2+cos(3x) in…

A: This question can be solved using the concept of area under curve.

Q: 2000 A television camera at ground level is 2000 feet away from the launching pad of a space rocket…

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Q: B2. dx Let g(?) = " 4t

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Q: 3x - - 4y 2xy 96

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

A: Since, the student has mentioned to solve only question number 2, so we are solving accordingly only…

Q: Solve the differential equation:+ y = e-* sin x 2

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Q: 5) Verify that the hypotheses of the Mean-Value Theorem are satisfied on the given interval, and…

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Q: ind the dimensions of the right circular cylinder of greatest volume that can be inscribed in a…

A: The figure inscribed in the sphere is needed to be maximized. So, volume of cylinder is to be…

Q: Find the equation for the tangent to the curve y = exp [2x] at the point (9, e 162). f(x) = exp [2x]

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Q: The variables x and y satisfy the relation 2 = 31-2x. (a) By taking logarithms, show that the graph…

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Q: 5. S sec(3x) tan(3x) dx

A: formula:∫ secx tanx dx =sec x +Cwe are given;I=∫ sec(3x) tan(3x) dx3x =t3 dx =dtdx =dt3

Q: Find the general solution: 9y" + 12y' + 4y = 0. 5.

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Q: X-axis. Consider the points P(3,0, 1), Q(5, –1,2), R(5, 1, – 1), and S(0, 4, 2). (a) Find the area…

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Q: For the given functions, find (fo g)(x) and (go f)(x) and the domain of each. 1(x) = 9(x) = 1-8x

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Q: r= -2 i+tj+(t2-1) k

A: