Evaluate the following indefinite and definite integrals using substitution.  Show all work, thank you!

Q: 5. Find two antiderivatives of f(x) = x0.8 - 3e²¹ + π cos(2x)

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Q: A particle moves according to the function s(t) = t³ - 3t² - 24t+5. When is the particle slowing…

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Q: Find the domain of f(x). f(x) = Interval 3x - 5 x² + 2x - 35 Answer Attempt 1 out of 2 2 Answer…

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Q: Question 1 (i) Determine dy/dx in the following: (ii) y = cos(x³ - 2x) y = x²-2 sin x y² −2(x+y)+x²…

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Q: Let g(x) = f(t)dt, where f is the function whose graph is shown. y f 20 (a) Evaluate g(0), g(4),…

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Q: A cup of coffee has cooled from 98°C to 50°C after 10 minutes in a room at 25°C. How long will it…

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Q: Find the area of the region between the curves y = x(1-x) and y = 4 from x=0 to x = 1.

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Q: 3 x¹ +1 dx

A: The given integral is (x4+1)/x2, limit from 1 to 3.

Q: Write v as the sum of two vectors, one in Span {u₁) and one in Span (u₂,43,44). Assume that…

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Q: Find the domain of the following function. f(x) = log 3 (x-4)

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Q: You are asked to write the quadratic function with the smallest possible integer coefficients that…

A: The given roots of equation are

Q: Find an antiderivative of the function g(x) = 6x³ +7. An antiderivative is

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Q: Find all exact solutions on the interval 0 <0 < 27. If there is more than one answer, enter them as…

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Q: A jewelry box with a square base is to be built with silver plated sides, nickel plated bottom and…

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Q: Use the Comparison Test to determine the convergence of the following series. n=1 n sin² n n³ + 1

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Q: As a preparation for the long bright summer days, Dr. Acula plans to store gourmet plasma in closed…

A: We have to use the concept of derivatives

Q: 17. The amount, A, of 108 grams of a certain radioactive material remaining after years can be found…

A: Given that the amount A of 108 grams of a certain radioactive material remaining after t years is

Q: Find an equation of the line tangent to the graph of G(x) = 3e The equation of the line is y=. at…

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Q: What is the second derivative x³ - 5x² + x = 0? A. 3x² - 5x B. 10x-5 C. 3x + 10 D. 6x-10

A: The given equation is Let

Q: 3x dx 1+e³x

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Q: Find all exact solutions on the interval 0 < 0 < 360°. If there is more than one answer, enter them…

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Q: 6. Find the first term (a,) and the common difference (d) for the arithmetic sequence: S5 = -105, a5…

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Q: Find the integral. Use C for the constant of integration. J cos(9t) sin(9t) dt

A: To find the following integral.

Q: 1. Find the area bounded by x = y²; x = −2y² +3

A: To find the area bounded by

Q: Consider the triangle below (not drawn to scale). ہے a= a Let b = 9, ZC = 40° and /A = 45°. Find the…

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Q: Sketch the slope field and sketch two solutions for the differential equation. (a)

A: Since you have posted multiple questions in a single request, we will solve first question for you.…

Q: 2. For the function g whose graph is shown, state the following. (b) lim g(x)= x-0 (a) lim g(x)=…

A: The graph of the function is given.The aim is to find the e)The equation of the vertical asymptotes.

Q: Consider the following function. g(x) = (x - 2)²-9 Step 3 of 4: Find two points on the graph of the…

A: Consider the function

Q: The graph of f(x) is given below. Select each true statement about the continuity of f(x) at x = 2.…

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Q: Find the intervals on which the graph off is concave upward, the intervals on which the graph off is…

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Q: Find an antiderivative of the function h(y) = 3y² — y6. An antiderivative is

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Q: Approximate the critical numbers of the function on the open interval shown in the graph. Determine…

A: The objective of the question is to identify the critical numbers of the function and determine the…

Q: Find the area A of the region that is bounded between the curve f(x) = −2 sin (2) over the interval…

A: Given that the region bounded by the functions  and  over the interval

Q: Consider the following integral. √1 + 7x dx Find a substitution to rewrite the integrand as du. u¹/3…

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Q: Solve the following problem and show your complete solutions. 1. Find the area bounded by x = y²; x…

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Q: 15 x² 3x 54 (Round the answer to four decimal places.) Find the area bounded by y = X- -, x = 3, x4,…

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Q: Find all of the real and imaginary zeros for the polynomial function. y=11x³-67x²+281x-25

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Q: A particular commodity has a price-demand equation given by p=√14,061 418x, where x is the amount in…

A: The price demand equation is given by  where x is the amount in pounds of the commodity demanded

Q: 5. The compound amount, 4, accrued with quarterly compounding ^=P(1+4)". where P is the principal, r…

A: To find the time it takes for the money to double with quarterly compounding, you can use the…

Q: 5. If f(5) = 7.8 and ƒ' (5) = 5.2, then use the linear approximation (also called the tangent line…

A: The linear approximation of a function f(x) at x=a is given by

Q: Use the graph to evaluate the limit. lim f(x) X→-1 X G

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Q: Find the critical numbers and the open intervals on which the function is increasing or decreasing.…

A: The objective of this question is to find the critical numbers and the open intervals on which the…

Q: f(x) = x² Which of the following is the linear approximation of f(x) at the point a=16? O O O 3…

A: f(x)=x3/8, a=16

Q: Find the exact location of all the relative and absolute extrema of the function. (Order your…

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Q: NASA launches a rocket at t=0 seconds. Suppose its height, in meters above sea-level, as a function…

A: The height function of the rocket is h=−4.9t2+205t+108 Here the objective is to find the peak of the…

Q: Consider the triangle below. Click on the picture to see it more clearly. If a = 8, the angle C =…

A: The given triangle has measures .The aim is to find the remaining meausres .

Q: Find the domain of the following function. √√x-5 X+2 G(x) =

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Q: Find an antiderivative of the function p(t) = t³ - 2 I t.

A: p(t)=t5−t42−t

Q: (f) (g) Find the absolute maximum and absolute minimum of g(x). On what interval(s) is g(x) concave…

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Q: Use the figures to calculate the left and right Riemann sums for f on the given interval and the…

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