1. Given f(x) = 1 and g(x) = "+¹, find the following functions and each of their domains. (a) (f+g)(x) (b) (4) (2) (c) (fog)(x)

Q: (ii) (x - ²)4

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Q: Q3, If Pix)= 1x5 + x³ % gxXx) = h(x) = f(x) + g(x). Determine if hex) is even or add function. 1 3 R

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Q: (a) Explain how we can test whether the DE (cos y) dx + (y² - x sin y)dy = 0 has an integral…

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Q: The polynomial of degree 4, P(x), has a root of multiplicity 2 at x = 2 and roots of multiplicity 1…

A: We need to write down the formula for the polynomial.

Q: Helium is pumped into a spherical balloon at a constant rate of 3 cubic feet per second. How fast is…

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Q: What is the IF, that can be used to solve the equation ty' + (2-4t)y=et cos (2t) OA. |u(t)= e3t-2t²…

A: Concept: The function chosen to solve the given differential equation is referred to as the…

Q: Find the local quadratic approximation of √x x = 1, and use that approximation to find the…

A: Given f(x)=xWe are required to findLocal quadratic approximation of f(x)=x at x0=1 Using the local…

Q: How to get the derivative of the 7th root of (5+2logz)9?

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Q: For a car traveling 60 km per hour (kph), the distance required to brake to a stop is normally…

A: Given, x~N(20, 32)

Q: Solve the following DE: (1+ y² + xy²) dx + (x²y + y + 2xy) dy=0 O 2x+y²(1+x)² = C O 2y² + x²(1+x)²=c…

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Q: Consider the function y = sin X on the interval [3, 9]. a) Find the slope of the secant line on this…

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Q: Find the indefinite integral by making a change of variables. (Hint: Let u be the denominator o…

A: ∫19+2xdx

Q: Given the differential equation (ysinx-cos²x) dx + cos x dy = 0 b. Solve the general solution of the…

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Q: Evaluate Σ 71-0 1 (2+i)

A: The given series ∑n=0∞12+in We have to find the sum of the series.

Q: Write an explicit formula for the sequence: 1 1 1 1 1 1 8 An 9 I 9 , 10 " 11' 12 , 13 ,

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Q: √2, and 4. Let a₁ = V an+1 = √2+ an Vn E N. Show that {an} is a monotone sequence by mathematical…

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Q: Find an equation of the tangent plane to the given surface at the specified point. z = ex − y + 7,…

A: See this solution in below

Q: Problem 2: Given the differential equation (y sin x - cos²x) dx + cos x dy = 0: a. Identify whether…

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Q: 5. a) What limit would you need toetaluate in order to find the slope of the graph cos(x) at the…

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Q: Determine the type of DE (select all that applies): 3x³y¹=2y (y-3) Exact Linear Separable None of…

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Q: The functions fand g are differentiable for all real numbers, x. The table below gives values of the…

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Q: d ri(t)= (31,-12+2,1-4) r2(1) = (3e', cos(t), t³-3). eir parametrized curves intersect at the point…

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Q: Determine the type of DE (select all that applies): 2xy dx + (y² + x²) dy=0 Linear Exact Separable…

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Q: (w³ + wz² − z dw + (z³ +w²z − w)dz = 0 3 3 - -

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Q: 3xydx+ (x² + y² )dy = C Answer: y² (4x² + y²)² = C²

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Q: Write an equation for a rational function whose graph has all of the indicated features:  -…

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Q: Question 3 2y dx + x[x²ln(y)-1] dy = 0

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Q: Set up a system of equations and then solve using inverse matrics. A manufacturer of portable tools…

A: we need to find the number of sets.

Q: graph of f' plotted in real time. f'(-9) = undefined f'(x) -10 -8 -6 -4 Answer: x = 15 10 5 -5 -10 y…

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Q: For the sequence an its first term is its second term is its third term is its fourth term is its…

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Q: A Moving to the next question prevents changes to this answer. Question 4 Given: y² + t² + (e2y +…

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Q: Given: y' + OA.0 OB. 1 OC. 2 OD. 1/2 OE. None 3 (1-2x)y and y(0) = 1, Find C

A: Given  differential equation:- y'+y3=131-2xy4

Q: 3 3 n(72) on the interval 2' 2 a) Find the slope of the secant line on this interval. (Round your…

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Q: Evaluate the integral S -5 ln(2x + 1) dx Note: Use an upper-case "C" for the constant of…

A: To find ∫-5ln(2x+1)dx

Q: Find a and b such that the function f(x) = {x² - 6x +10 [x² - 6x +10 if x≤-1 if x>-1 Is…

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Q: 9 (5) Let f(x,y)=+=+y+=+5 (a) Find the critical point(s).

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Q: If y = g(x) solves the initial value problem (IVP) Sy' = 4x + 12, y(0) = 20, and (x,y) is the…

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Q: Given f(x) is a continuous function. If f(- 9) = 6 and f'(x) ≥ 8 for -9 ≤x≤ smallest f(-3) can…

A: The objective is to find the smallest value of f(-3) which can be possible.

Q: 5. Determine the equation of the tangent to f(x)=2x-2 where x = 3

A: The given function is  f(x)= 2x-1x-2 Find the equation of tangent line at x=3.

Q: 2. For each of the following functions, determine the derivative using only algebraic techniques and…

A: I am attaching image so that you understand each and every step.

Q: 1 ns a) y = -x4q-omantics is now maxs oris no viiperib zmolizoup on lis 19war ni bobned od reum…

A: Since you have asked multiple question, we will solve the first question for you as per our guide…

Q: Find the general solution

A: Here we have to solve the differential equation.

Q: For the sequence an = its first term is its second term is its third term is its fourth term is its…

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Q: Find the linear speed of a point moving with uniform circular motion, if the point covers a…

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Q: at x = 7/6 = 7/6 for f(x) = cos(x).

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Q: Solve the following DE: (x²+1) dx + x²y² dy=0 Oxy³ = 2(1+Cx+x²) Oxy³=3(1+ Cx-x²) O xy2=2(3+…

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Q: Given: y' +=(1-2x)y4 and y(0) = 1, Find C OA.0 B. 1 OC. 2 OD. 1/2 OE. None

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Q: Use the unit cirle and the fact that sine is an odd function and cosine is an even function to find…

A: Given query is to find the value of the sine function.

Q: Find the decomposition of a(t) into tangential and normal components at the point indicated. r(t) =…

A: The given data is: rt=3-t, t+4, t2, t=2 Therefore, r→t=3-ti+t+4j+t2k       ......1 Differentiate…

Q: Find y' and y" for x² + 2xy − 3y² = 41. Simplify. -2x - 2y 2x - 6y y" = help (formulas) y' help…

A: Given query is to find the second derivative of the expression