Use properties of limits and algebraic methods to find the limit, if it exists. (If the limit is infinite, enter '∞' or '-∞', as appropriate. If the limit does not otherwise exist, enter DNE.) lim x→−1/2  6x − 8 8x2 + 6

Q: Book Problem 31 Find a function f and a positive number a such that f(x): a = = + [² 2+ f(t) dt =…

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Q: Solve the given differential equation. All solutions should be found. 3x² - 3y - y³ 3x + 3xy² dy dx…

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Q: Simplify: 3√2 + √32

A: Given.

Q: Suppose f(x) and f'(x) have the following values. -7 -6 -5 -4 -3 4 -9 1 9 2 6 x f(x) -2 f'(x) 1 -2 3…

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Q: Bioavailability is a term that refers to the fraction of an antibiotic dose taken orally that is…

A: Given problem:- Bioavailability is a term that refers to the fraction of an antibiotic dose taken…

Q: 1. Sketch the graph of the equation. x2 + y2 + 10x − 4y + 29 = 0   2. Complete the graph using the…

A: Given problems:- 1. Sketch the graph of the equation. x2 + y2 + 10x − 4y + 29 = 0 2. Complete the…

Q: lim A) e⁹ TE B)e-9 C) D) e-s

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Q: 25. lim h→0 (x+h)² +4(x+h) —x²− 4 at h (A) x³ + x4 (B) x² + 4x (C) 2x+4 (D) nonexistent

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Q: If A = 1=1 ²₁₂ 21₁B =[ ²¹/₂ 3 b) B.A c) A-2B a) 3A-C 3] -2 = [3²5] 4J and C= Find:

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Q: Evaluating a Function Evaluate the difference quotient and simplify the result f(x) = x² - 7x + 3 0…

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Q: x-2 lim x-2 √2x2+1-3

A: Given,            limx→2x-22x2+1-3

Q: Label the zeros and asymptotes. Graph each function. Answer each limit question. 11.…

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Q: 1. Find an equation of the circle that satisfies the given conditions. (Use the variables x and y.)…

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Q: (3) Find explicit particular solutions of the initial value problems below. (a) + 1 = 2y, y(1) = 1.…

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Q: Find the exact arc length of the curve over the stated interval. y=x²³ from x=1 to x=8

A: Please see the below picture for detailed solution.

Q: If f(x) = (cos(√) - In (x²))³, then f'(x) = 3

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Q: Find the limit of the function lim x → − 6 ( 2 x + 12 | x + 6 | )

A: Find the limit

Q: Evaluate the integral: ³√1 + 100x² da

A: Need to find out the integration.

Q: Find all minors and cofactors of the matrix. -1 2 3 6 45 3-1 2 (a) Find all minors of the matrix M…

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Q: 2. Describe how the graph of y = 2ƒ (²x) — 3can be produced from the graph of y = f(x). List all

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Q: f(x) = y 9 8 7 6 5 4 3 2 x + 5 J 5 6 7 8 X 1 2 3 4 Describe the interval(s) on which the function is…

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Q: 2. y' ysecx

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Q: lim sec O 0→→→I+ 2

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Q: Solve the following differential equation x² (y² +3) = 0 y(x³ +1) dy 3. + dx 4. xdx e-x + (y+1)dy =…

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Q: If y = arcsin(- 5x + 1), dy dr

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Q: The acceleration function for a particle moving along a line is a(t) = 2t + 4. The initial velocity…

A: We need to find velocity and distance.

Q: Question 1.7 of 25 The area of the region that enclosed by f(x) = 2x-x² and y = 0 B) / A) 413 c) 3/4…

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Q: If an investment increases 1% the first year, 5% the second year and 9% the third year, what is the…

A: Let the investment at starting is = x   Increase in first year =1 % increase in second year = 5%…

Q: 4. a) If you were given a function in the form y = g(x), explain how you would determine the…

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Q: Let C be the positively oriented circle x² + y² = 1. Use Green's Theorem to evaluate the line…

A: Greens theorem

Q: Which of the following is the appropriate substitution for the Bernoulli differential equation xdy +…

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Q: lim x→0 (sin3x sin5x/x2)

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Q: Sketch the region and find its area. The region bounded by y = -8 00 8 Y -00 X 36 9+x² Calculate the…

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Q: Solve (xy + 4a²y)dy = √(xy-5a³ + ax - 5a²y)dx

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Q: (x²-1, x0 Determine the domain and range.

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Q: 13. f(x)2(x-4Xx+3y³ a. b. C. lim x-2+ f(x) = f(x) =

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Q: How would you "remove the discontinuity" of f? In other words, how would you define f(4) in order to…

A: Discontinuity of f can be removed by factorisation of the numerator

Q: A- Find (1) asymptotes for the following functions: x²-1 x²+2 (2) x³+x²-x-3 x²-1 x²-4 (1) f(x) =…

A: Note: Since, the student has posted four sub-parts with numbering (1) and (2). We are considering…

Q: Eliminate the arbitrary constant. y=Ax 5+ Bx³ A B 7xy "- x²y + 15y = 0 D x²y '- 7xy "+15y = 0…

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Q: y = x ² √√9-x² = x²(9-x²) ¹/2 WwS =/0²7 xF-P y² = x² [² (9-x²) ²¹/²2 (2x)] + (9-x²) ¹2 (2x)

A: NOTE: Refresh your page if you can't see any equations. . take derivative

Q: Use the definition of Taylor series to find the Taylor series (centered at c) for the function. f(x)…

A: To Find: The Taylor Series of f(x)= lnx with center c= 1

Q: 2. Solve the initial value problem x' = (t+1)/√t, x(1) = 4.

A: Given, x'=t+1t, x(1)=4

Q: 1. Calculate dy da for the following: (a) y ln(x + 2x³ - 6), =

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Q: 17. f(x)=- a. b. C. d. lim lim (x-2) lim f(x)= lim x-2 /(x)= f(x) =

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Q: Prove the identity. sin (x-y) cosx cosy tan.x - tany Note that each Statement must be based on a…

A: We can prove the given statement as per the example in the below steps.

Q: 14. Evaluate to 4 decimal places: csc 153°

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Q: The inflection point of the graph f(x) = (x + 1)tan ¹(x) is B) (0,0) C) (-1,0) A) (15) D) (0,1) E)…

A: inflection point of the function f(x)=x+1tan-1x

Q: x³+4x²+x-6 3 sin(-x)+3x² et f be the function defined at f(x)

A: Function

Q: Find the solution of the given initial value problem. ty' + 4y = t²t+7, y(1) = 8, t > 0 y =

A: This differential equation can be solved as follows:

Q: 15. Let 2 √x 4 3/2 y' = 2y + 2xy' 13/2 Solve for y' when x = 1 and y = 4

A: NOTE: Refresh your page if you can't see any equations. . here we have x=1 and y=4