Find the X-intercepts (x,y) and y-intercept (x,y) and the vertical and horizontal asymptotes. 2.Describe the end behavior of the function.

Q: 4. Solve the following equation by completing the square. Be sure to show all steps. (round answers…

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Q: Find the equation of y, given the derivative and the indicated point on the curve. dy dx = 2x - 1 y…

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Q: For the linear function y = f(x) df dx a. Find at x = 8. ƒ'(8) = b. Find a formula for x = f-1(y).…

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Q: If f(x) = f'(x) = 4-3x7, find f'(x). Use exact values.

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Q: Find the arc length of the graph of the function f(x) = ln(cos(x)) ㅠ π [153, 5 Use the tables to…

A: Arc length of y=f(x) on a, b is  L=∫ab1+f'x2dx We have f(x)=lncosx given interval π9,π5

Q: 1. Use the Mean Value theorem to show that for any two real numbers a and b, we have | sin b - sin a…

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Q: Given r(t) = (set, et cos(t), et sin(t)), determine each of the following. (a) the unit tangent…

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Q: Let f(x) x³ + 6x² 36x +11. = (a) Use the definition of a derivative or the derivative rules to find…

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Q: The position function of an object is given by r(t) = (t2, 8t, t²- 28t). At what time is the speed a…

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Q: 2. If f: R→→ R satisfies f(1) = 3 and f'(x) ≥2 for all x's, how small can f(7) be?

A: Here we have to find the smallest value of f(7).

Q: Suppose p′(−1)=−2 and q′(−1)=−5.5.  If r(x)=−7p(x)+10q(x), find r′(−1).

A: We have to find the value of r'(-1).

Q: 7 Write a limit using summations that would equal S Answer: lim N→∞ n k=1 [x³ - 4] dx. Submi

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Q: Solve the separable differential equation dx 2 dt and find the particular solution satisfying the…

A: Please see the below picture for detailed solution.

Q: Evaluate the indefinite integral sin² t cos³ tdt = + C

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Q: Find the limit, if it exists. 4x² lim X--X+2

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Q: -6-5-4-3-2-1 у 7г 6 4 3 2 1- -1 -2 -3 -4 -5 -6F 1 2 3 4 5 6

A: Range :- all the y value where function is defined

Q: What is the indefinite integral (anti-derivative) { cos(x) dx? ○ sin(x) + C cos(x) + C - sin(x) + C…

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Q: Evaluate the definite integral. Use a graphing utility to verify your result. 9 [(u - 2) du Submit…

A: Topic:- application of integration

Q: Solve (x² 1 + 2y) dx + (1 - x²) dy = 0; when x = 2, y = 1 1) (x + 1 + 2 ln x 1|) b. (x + 1) y = (x −…

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Q: 4) Find the equation of the line tangent to h(x) = (2-x)(x³ +4x-4) at x=1.

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Q: Find the values of x, y and z that correspond to the critical point of the function 2 = f(x, y) =…

A: The given function fx,y=4x2+8x+7y+3y2 To find the critical points of the function

Q: 15 Lo - - dx 15 X (x + 1) ²/ O 0 O or| 800 88 O 1 O 176 5

A: The answer is 0.

Q: (-1,1) a N (1,1) 2

A: find the domain and range of the given graph Domain: set of x values for given function Range : set…

Q: cos² xy' = (1 + y²)

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Q: (2xy + y) dx + x (x + 1) dy = (x² - 1)dx

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Q: What is the max area of a rectangle placed between the x-axis and the function f(x)= -x^4 + 3

A: To determine the maximum area of a rectangle placed between the x‐axis and the function fx=-x4+3.

Q: Use interval notation to determine where f(x)>0. 2. Use interval notation to determine where f(x)>6.…

A: The objective is to use interval notation to determine where f(x)>0. 2 and use interval notation…

Q: 12 76 Exercises (if possib 15. y = 5x + 3 17. y = -x - 1 19. y − 5 = 0 0 1 23. 7x - 6y = 30 020…

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Q: Consider the function f(x) = x 52+4 x + 1 a. Find the first derivative. f'(x) = b. List any critical…

A: As per our guidelines we are supposed to answer only first three parts. Kindly repost other parts as…

Q: Evaluate the integral using the following values. [x³ dx = 260, x 29 - ·[³x dx = 10, [³dx = 2 (29 -…

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Q: Calculate r' (t) and T(t), where T'(t) = ( T(t) = { r(t) = (8+t, (9+t), 2+2t). ).

A: Given vector function r(t)=8+t, -9-t, 2+2t

Q: 3. A particle moves along the x-axis with velocity v(t) = t2-1, with t measured in seconds and v(t)…

A: Given velocity v(t)=t2-1 To get the total distance traveled, we have to integrate the velocity…

Q: Find the Domain and Range of the function (Have your answers in interval notation)

A: Question: Find the Domain and Range of the function (Have your answers in interval notation)

Q: Calculate: fx²e³dx

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Q: Compute the length of the curve r(t) = (-4t, 5t — 3, -2t + 3) over the interval 0 ≤ t ≤9 L =

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Q: Let ƒ(x) = x³ + 3x² − 9x + 22. (a) Use the definition of a derivative or the derivative rules to…

A: The given function fx=x3+3x2-9x+22 use the derivative formulas, ddxxn=nxn-1ddxax=addxa=0 where, a be…

Q: The angle between two vectors a = (1, 1, 2) and b = (-1, 2, k) is 60°. Find the value(s) of

A: Topic:- application of vector algebra

Q: Given the function f(x) = −4 sin³ x, find ƒ'(x).

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Q: Find the solution to satisfying _y(t) = dy dt = 2y y(6) = 9

A: The given differential equation is; dydt=2y As we know from the integral rule,  ∫1ax+bdx=1alnax+b+C

Q: Evaluate the integral below by interpreting it in terms of areas in the figure. The areas of the…

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Q: Given the curve shown below, determine if the slope of the curve at x = negative, or zero. 4 3 2 O…

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Q: Find the curvature (t) of the curve r(t) = (−4 sin t) i + (−4 sin t)j + (1 cost) k

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Q: Find the indefinite integral. (Remember to use absolute values where appropriate. Use C for the…

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Q: f(x) = = -2x² + 7 7x - 10 if x -1

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Q: The graph of the function f(x) is shown below. State all values of x in the ope which the function…

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Q: -10 -5 f(x) 10 10 5 10

A: Note: Since the student has posted 2 sub-parts of the question in which the part (1) is complete and…

Q: A right triangle has legs of 30 inches and 40 inches whose sides are changing. The short leg is…

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Q: 1 The length of the curve y = x³ + x¹ from x = 3 to x = 4 is: a. b. C. d. 145 16 257 12 99 8 593 48

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Q: A fast-food restaurant has a cost of production C(x) = 14x + 108 and a revenue function R(x) = 82.…

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Q: Find the average value fave of f(x) = x³ between -1 and 1, then find a number c in [-1,1] where f(c)…

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