Activity 5: Find the following indefinite integrals. 1. Sdy 2. fx(8x? – 6 +) dx 3 6. S COSX dx sin?x 7. S(-6 cos x + 4 sin x) dx 8. S cot?x dx 9. S 3. S 1+x+x? dx 4 sin x dx 3 tan x 4. S(8x4 + 4x3 – 6x2 - 4x + 5) dx 5. S(7 cos x + 4e% + e)dx x20+x3-x dx 10. S x4

Q: 25. Find the constant(s) c for which the function f(x) is continuous on (-∞,+ ∞) (c? — х2 , х<2 12…

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Q: Find the equation of the tangent line at the given point on the following curve. 3 3 In (x+y)=x y" +…

A: The given equation is  ln(x+y)=x3y3+ln(x2+2)-8, (1,2).

Q: The integral in this exercise converges. Evaluate the integral without using a table. 14 dx V196 -…

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Q: sin(z) Find the derivative of the funciton F(x) = In(1 + 6v) dv. F'(x) =

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Q: Y = 1 - x², y = 2 + 2x, and y = 2– 2x

A: Let's find.

Q: Determine the Taylor polynomial of degree 3 for the solution to the initial value problem 1 y' x + y…

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Q: Expand the quotient by partial fractions. x² +1 x - 17x+72 x +1 x - 17x+72 (Simplify your answer.)

A: To expand the quotient by partial fractions.

Q: d for cheese in a particular country for mplicit equation fa unit of cheese and D represents a ce a…

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Q: x – 2 - Let g(x) x + 3 (a) Find the third degree Maclaurin polynomial of g- (b) Approximate g(0.2)…

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Q: If f(x) dx = 2 and f(x) dx = 7 then f(x) dx equals a -4 b. 4 -5 O O O

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Q: 2. Compute the scalar line integral xy ds where C is the part of the circle of radius 2, centered at…

A: Put x=2cost , y=2sint

Q: Use D-I method

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Q: dy Find dx by implicit differentiation for the following equation. 2.5 x+ In y =x dy

A: We have to find dy/dx for the given function.

Q: In Exercises 22 through 24, find an equation of the sphere satisfying the given conditions. 22. A…

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Q: Determine the maximum value of f (x) = 5x – e5x [T:3] on the interval [-1,1] %3D

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Q: Integration by Trigonometric Subshtunon SxCx?- ax+4) $12 XP

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Q: 1. 3 Consider the parametric surface 7(u, v) = (2uv, u? - v, u² +v²), where u +v < 2. Evaluate the…

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Q: Find all the orginal funchians of the funckion fryl=2y (y-s)²

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Q: For numbers 17– 20, use the given function. (5 + 2x, x <- 6 f(x) = } x + 5, x 2– 6 17. What is the…

A: From given function we have to find out  f ( - 6 ) &amp; value of  right hand limit at x = - 6 to…

Q: 13. Prove that the three points (-3, 2, 4), (6, 1, 2), and (-12, 3, 6) are collinear by using the…

A: To solve the following problem

Q: Suppose that a particluar funciton f satisfies f" (x) = - (4 sin(x) + cos(x)), f(0) = 3, f'(0) = 5.…

A: f"(x) = -(4sinx +cosx) ,  f(0) = 3 , f'(0) =5 now integrate the f"(x) f'(x) =4cosx -4sinx +c now…

Q: The piecewise function f(x) is graphed below. Use geometric formulas to evaluate the following…

A: From the given graph;

Q: Suppose that L is a location function of an object, given as L(t) = We will compute the 3t + 7…

A: We can solve this as follows:

Q: Use the Ratio Test to determine the radius of convergence of x" Σ Vn : 11" n=1 Then determine…

A: Let's find.

Q: A radioactive substance decays at a continuous rate of 17% per day.  After 8 days, what amount of…

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Q: -Obtain the Cartesian equation of the curve by eliminating the parameter. 14) x = t - 3, y = t2 + 5…

A: To obtain the Cartesian equation of the given curve.

Q: If m s f(x) < M for a s x s b, where m is the absolute minimum and M is the absolute maximum of f on…

A: Given problem:-

Q: 6.26. у - 3у %3D0

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Q: Find the most general antiderivative or indefinite integral. Use a capital letter C to denote an…

A: Solution of question is written in below steps.

Q: Find the most general antiderivative or indefinite integral. Use a capital letter C to denote an…

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Q: For each item, find an equation of the plane with the given properties: (a) containing the points…

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Q: Solve the exponential equation for t. Round your answer to three decimal places if necessary.…

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Q: dy 7. S- y vy2 -6y + 5

A: Here we have to integrate the given Integral.

Q: dx 1+x3

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Q: 16 A scientist found the number of bacteria (y) after (t) minutes can be estimated by the following…

A: We can solve as follows

Q: K to to Match each equation with a graph above O 2(0.72)" a. blue (B) O 2(1.2)" O 2(0.81)" O 4(1.2)"…

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Q: Determine whether the given differential equations are homogenous and, if so, solve them. 2x + y…

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Q: x2 dx (3x3-4)5

A: We need to evaluate integral.

Q: 27. Find an equation of the sphere satisfying the ff. a. The vertices of a cube are on the sphere,…

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Q: Given the following velocity function of an object moving along a line, find the position function…

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Q: Match the graph to one of the polar equations. 3) -5 4 -3-2 1 2/3 4 5 1 -4+ 1.

A: This is aproblem related to polar equation calculation. We will assume, x=rsintheta and y=rcostheta

Q: How 3 Find the absalute maxine and minima for the funCtion (4x-x) Cosy an the rectangular plate…

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Q: 2. Given : f(x) = {x² - 3, x+3 6, %3D X = 3

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Q: 37. Let y = uv be the product of the functions u and v. Find y'(2) if u(2) = 7, u'(2) = 4, v(2) =- 5…

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Q: Solve for æ: 109z - 2 = 710z – 6

A: To solve for x.

Q: Sind the absolute maximum and the absolute minimum of f(x,y) = 2x – 2xy+y whose domain is the region…

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Q: Find dy far y= dx

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Q: х—1 dx х4—1

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Q: Use left-endpoint approximation to approximate the area under the curve f(x) = – 0.3x + 25 between x…

A: Let's find.

Q: xsin-1x dx V1-x2

A: We know, ∫udv=uv-∫u'vdv ddxsin-1x=11-x2