1) One-sided limits If lim, o f(x) = A and lim, o f(x) = B, find a. lim, o f(x³ - x) f(x³ - x) b. lim, o c. lim, o f (x² - ¹)

Q: xy'= y inx

A: xy'=ylnx

Q: or For the given function f(x) and numbers L, c, and e> 0, find an open interval about c on which…

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Q: Consider the function below. f(x, y) = In(x + y - 3) (a) Evaluate f(1, 3). (b) Evaluate f(e, 3) (c)…

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Q: MULTIPLE CHOICE 1. Let f(x) = x² + 2x - 5. What is the x-coordinate of a point where the…

A: Let fx=x3+2x-5. To determine the x‐coordinate of a point where the instantaneous rate of change of f…

Q: Decide whether the limit exists. If it exists, find its value. lim f(x) x-1 02 -- 01 3+ 2 Ⓡ O Does…

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Q: (6x+y²) dx + (2xy-3y²) dy =o

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Q: pls

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Q: 2. Obtain the general solution. (Let 2C=C) (4x + xy²)dx + (y + x²y)dy = 0

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Q: (k/x². x 2 -1 < x≤2 x ≤-1

A: If the function is continuos at a point then the left hand limit and right hand limit of the…

Q: 4. A boat is pushed off from a beach at 2m/sec. A man on shore holds a rope, tied to the boat, at a…

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Q: . Find the solution of the DE y' a. 2xy + Iny = c b. -2 /y-2lny = c c. 2xy + 2lny = k d. -2y+lny = c…

A: The given differential equation is; y'=y/[x+sqrt(xy)].

Q: the distance between points P (5,-4) and R (-1,4)?

A: Given query is to find the distance between the points l.

Q: 3. Find d² d02 sin Ꮎ (1 1+ cos 0 Simplify your answer.

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Q: Which of the following is an equation of the tangent line to the graph h(x)=- Oy-3--1(x-3) Oy - 1/2…

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Q: Q3/ Use the l'Hopital's rule to find the limits 1) lim X-0 sinx-x x3

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Q: Find the length of the curve. 8(1) - (48, 1², 12³). r(t) = Osts 1

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Q: The x-coordinate of a particle in curvilinear motion is given by x = 4.9t³-5.2t where x is in feet…

A: We have to find v and a.

Q: Identify and sketch the domain of f(x,y) = √4x²-y In x

A: We know, The function ln x defined for x≥0 The function x-a is defined for x≥a

Q: Let C be the curve of intersection of the parabolic cylinder x² = 2y, and the surface 3z = xy. Find…

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Q: Find the instantaneous rate of change of the function f(x) = x3 + 8x when x = –3

A: Find the instantaneous rate of change of the function f(x) = x3 + 8x when x = –3

Q: 10. Given the graph below is f(x). Draw the graph of the slope f'(x) 5 4- 3 2 1 0 -4-3-2-1,0 1/2 3 4…

A: Solution is here

Q: Find an equation for the line tangent to the curve y =(√x - 9)(x5 + 8) at x = 1. y =

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Q: If f(x) = f'(x) = 9x + 2 x² +4 - I compute f'(x). 9x² + 4x+36 (x²+4)² X

A: Finding f'(x)

Q: CLASSIFICATION OF DIFFERENTIAL EQUATIONS Classify each of the following differential equations by…

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Q: ind a value of h for which 3.0 2.5 h = o in y 2.0 1.5 1.0+ 0.5 f(2+h)-f(2) h 0.5 1.0 Give your…

A: Given Graph:-

Q: and the 1st derivative of x³ + y³ - 6xy = 0

A: Topic: - application of derivatives

Q: 7/2 4 cos 0 3+2sin -de 0 30

A: Note:- Since you have asked multiple question As per our policy, we will solve the first question…

Q: 4. y = A + Bx + Cx² + 2x³

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Q: Let f(x) = = 52 – 3 if a 4 - -6x+b if x > 4 If f(x) is a function which is continuous everywhere,…

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Q: Find the average rate of change for the function over the given interval. y = 3 between x = 1 and x…

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Q: The graph of the function f satisfies lim f(x): = x→4 -3 -18 f(x) 2 7 - Note: You can click on the…

A: First we find equation of given function. Given function is a straight line.

Q: f(x, y) S (y + 2x²)² x² + y² 0 lim Show that (x,y) (0,0) si (x, y) = (0,0) si (x, y) = (0,0). f (x,…

A: Given function : f(x,y)=(y+2x2)2x4+y2    for (x,y)≠(0,0)0                    for (x,y)=(0,0)

Q: -7x lim 200 2+ 2x 15x-9 lim 1-∞ 2³ + 3x - 15 lim 818 lim 818 = r² - 2x - 10 7-13x2 lim 8118 T²+ 13x…

A: Concept: Unique real numbers are limits in mathematics. Take into account a real number "c" and a…

Q: Evaluate ㅠ * 0 sin (9x) sin(5x) dx.

A: To evaluate the following integral.∫0π sin9x sin5x dx

Q: 1. Find the equation of the plane that passes through the points (1,0,-1), (0,2,3) and (0,0,5) in R³…

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Q: 23-2 y₁ Evaluate. lim f(x) x--3

A: Given query is to find indicated limit.

Q: L = 27M³ + 19N0² + MNO Find 62L 6 MGM

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Q: Is f(s, t, z) = st²e-² a solution to the differential equation: fzss=2fzzftt - (ftz)²

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Q: Evaluate lim x-2+ 2x + [2x] x² + x - 2 and lim x+ 2 2x + [2x] x²+x-2

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Q: f(x, y) = x² - 2x +1+3y².

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Q: Solve (a) dy +2 = 4x²; y(1) = 2, (b) av' - 4y = x, (c) dr = (d) dx + 2y cot a = csc a. = 3(y +…

A: Solution is given below:

Q: The table shows the position of a motorcyclist after accelerating from rest. t (seconds) (ii) (1)…

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Q: Please answer question 72

A: We have to find the area of the shaded region.

Q: EXAMPLE 4 Find the derivative of the function f(x) = x² - 3x + 5 at the number a. SOLUTION From the…

A: Finding the derivative using the definition

Q: Solve dy/dx = x² + 2xy + y² + 2x + 2y, y(0) = 0.

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Q: and sketch its graph. Label all criti 1 c) f (x) = xe-*

A: Given problem:- fx=xe-x

Q: 1. Eliminate the arbitrary constant. y² = 4C(x + C)

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Q: determine the general equation of the tangent plane to the surface of parametric equations: x = 1 +…

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Q: if x - 2 Calculate the following limits. Enter "DNE" if the limit does not exist, or "oo" or "-oo"…

A: Here, the given function is: f(x)=-4x+2 if x&lt;-24x+8 if x&gt;-2

Q: Suppose that the functions u and w are defined as follows. u(x)=x+2 w(x) = x² 2 Find the following.

A: NOTE: Refresh your page if you can't see any equations. . . take x=-4