Simplify as completely as In e + 2 ln x possible. Write it as a single logarithm whose coefficient is 1.

Q: The area of the surface obtained by rotating the portion of the curvey = sin(x) where evaluating the…

A: We need to set up surface area integral.

Q: -10 -6 -2 10- Y 8- 6 44 -2- -4 -6- -8- Select the correct answer below: 8 Identify where f'(x) < 0…

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Q: Question 12 (D² + 2D + 5) y = 6sin2x + 7cos2x

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Q: Suppose and y are related by the equation xy = 2x, where y is a function of x. dy dx 2. Use implicit…

A: Topic = Derivative

Q: Which of the following is equivalent to (A) (B C (D L² (x5 - - 4x + 6) dx [² (2³-42) (x5 - 4x³+6) dx…

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Q: If f(x) = x - 8x² and h = 0, find the following and sim (a) f(x + h) = (b) f(x +h)-f(x) h Bund

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Q: The graph of f(x) = -² 3r is shown alongside. a Use the graph to estimate the gradient of the…

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Q: he birth rate of a population is b(t) = 2000e0.021t people per year and the death rate is d(t)=…

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Q: Find the maximum and minimum values of the function g(0) = 30 – 6 sin(0) on the interval [0, [0, 1]…

A: The given function is: gθ=3θ-6sinθ   For maximum and minimum value, differentiate the function and…

Q: Question 16 (D² - 2D + 1) y = 2xe²x + 6ex

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Q: For f(x) = 2√x and g(x) = xª + 6, find the following. (a) (fog)(x) (b) (gof)(x) (c) f(f(x)) (d)…

A: The given functions, fx=2x and gx=x4+6. We have to find the required composite functions.

Q: f'(x) = Differentiate the function f(x)=x197 +19.7.

A: Explanation of the answer is as follows

Q: f sin(5 - 6x) sin (6x + 5) dx

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Q: If f(x) = 7x² - x + 5 and h = 0, find the following and simplify. (a) f(x + h) (b) f(x+h)-f(x) h ||

A: a) Replace x by (x+h). b) Substitute the required.

Q: Find the area of the shaded region. A = -6 y = x³ - 15 x (-4,-4) X y 20 10 -10 -20 2 (4,4) y = x 4 6…

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Q: In the derivative, transform into linear equation y = mx + b (the form)

A: Given :  y = mx + b (the form)   To find : In the derivative, transform into linear equation

Q: Use the following information to complete parts a. and b. below. f(x) = 5√/1+x; approximate $√√1.16…

A: We know that the Taylor series of fx centered at 0 is given by fx = f0 + f'01!x + f''02!x2 +…

Q: Consider f(x) = x5 - 15x³. In this question you will find the local minimums and maximums of f (x),…

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Q: Determine the type of DE: 2xydx + (y²+x2) dy=0 Homogeneous Bernoulli's equation Both Homogeneous and…

A: The given differential equation is; 2xydx+(y2+x2)dy=0.

Q: Two cars, A and B, start side by side and accelerate from rest. The figure shows the graphs of their…

A: In order to find the time at which the cars are again side by side, obtain the total numbers of…

Q: Consider the parametric equations below. x=?-4, y=b+ (a) Sketch the curve by using the parametric…

A: NOTE: Refresh your page if you can't see any equations. . given equations are

Q: Let f(x) = e* and g(x) = Inx. Then O(A) x ER such that f(g(x)) = g(f(x)) O(B) Vx ER, f(g(x)) =…

A: The answer is given below:

Q: Suppose f and g are continuous functions such that g(3) = 3 and_lim [3f(x) + f(x)g(x)] = 36. Find…

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Q: differential equations 2ycos(2x)dx+(sen(2x)-2sen(y))dy=0

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Q: Find the equation of the tangent line to the graph of f(x) = √√√/2 x at (1,1). Your equation must be…

A: We need to find the equation of tangent to the graph f(x)=2-x at point (1,1).

Q: 105 105 Suppose that a; = 17 and b₁ = 26. Compute the sum. i=1 i=1 105 Σ (30a; + 29b;) i=1

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Q: Find a power series representation centered at 0 for the following function using known power…

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Q: Determine whether the following series converges. Justify your answer. ∞ Σ k=1 8 + cos 5k k8

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Q: Evaluate the definite integral. 3 fox (9x² + x−¹) dx

A: Given, ∫139x2+x-1dx

Q: Rewrite the expression as a sum or difference, then simplify if possible. 10 sin(7x) cos(6x) =…

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Q: 1) Given that csc A each of the following: a) sec B b) cos (A + B) c) sin 2A and cot B = where - <A…

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Q: The volume of the solid generated by revolving the area in the first quadrant bounded by y = e + 1…

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Q: U.S. Internet advertising revenue grew at the rate of R(t) = 0.82t + 1.14    (0 ≤ t ≤ 4) billion…

A: NOTE: Refresh your page if you can't see any equations. . U.S. Internet advertising revenue grew at…

Q: Nutrition   A certain company′s Mixed Cereal for Baby contains, in each serving, 80 calories and 10…

A: This is a linear programming problem. Here, we will first find the system of inequality, then graph…

Q: Consider the function f(x) = 5 - 7x², -3 ≤ x ≤ 2. The absolute maximum value is and this occurs at x…

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Q: Use the Ratio Test or the Root Test to determine if the following series converges absolutely or…

A: We need to use the ratio test to test the convergence.

Q: The function y = f(x) is given by the figure. 2 1 0 -1 -2 y 1 B(x) = 2 y = f(x) 3 4 f(t) dt 5 6 Find…

A: Using the given graph we need to find the maximu and minimum value of:B(x)=∫3x f(t) dt

Q: 6. Find the directional derivative of the function ƒ (x, y) = x² + x sin (y) at the point (1,7) in…

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Q: Suppose I want to use a "u" Substitution to find f cos x(sin x) dx . What should I choose for u?

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Q: Consider the infinite series k=1 1 k + 3 Evaluate the first four terms of the sequence of partial…

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Q: Nov 16, 5:52:16 PM A particle moves along the x-axis with velocity given by v(t) = cos (t) for…

A: Given query is to find partical moving away of toward the origin.

Q: Which of the following is equivalent to of √² (92³ - 2 √² + +9) dz B ® √ √edz [(92²-2√2+ A 9x³ [(9x²…

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Q: (5) (6) (7) მე-2 d'y dx² Ərət Ət² √5 + sin x sin 0 = (2-y)dx + (2x − 3y)dy = 0 - d³y d03 cos dy do =…

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Q: se a calculator to approximate the degree measure (to 1 decimal place) of the angle 0 subject to the…

A: Given query is to find measure of indicated angle.

Q: Give a parameterization for the surface z F(u, v) = (u, v, ). x² - y²: = x

A: NOTE: Refresh your page if you can't see any equations. . the given surface is

Q: Suppose that the second derivative of the function y = f(x) is y'' = (x + 1)(x-2). For what x-values…

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Q: If y = f(x) in the figure, find the following. y -6 -4 -2 (a) f(5) = (b) f(9) = 12 6 -6- (5, 6)…

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Q: Determine the type of DE: - − ydx + (x + √xy) dy = 0 Homogeneous Bernoulli's equation Both…

A: To determine the type of the following DE:-y dx+x+xy dy=0

Q: Show complete solution.

A:

Q: A. For each differential equation, give the dependent and independent variable(s), state whether the…

A: CONCEPT OF DEGREE:  The degree of the differential equation is represented by the power of the…