Find the limit L. Then use the - definition to prove that the limit is L. lim (x²+4) X→ 1 L =

Q: ind the speed over the path r(t) = (sinh t, sinh t, 9t) at t = 3. Jse decimal notation. Give your…

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Q: 65. Finding slope locations Let f(x) = 2x³ - 3x² - 12x + 4. - a. Find all points on the graph of f…

A: Given:

Q: Determine all intervals on which the graph of f is increasing. -8 7 -6 -5 -4 3-2-1 5 4 3 2 -1 -2 -4…

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Q: ót TT 64 on 3 L L de de 5 6 V= 8 10 The graph above shows the base of an object. Compute the exact…

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Q: Find a formula for a function lim f(x) = 0, lim f(x) = 00, that satisfies the following conditions.…

A: limx→±∞f(x)=0,limx→0f(x)=−∞,f(3)=0, limx→9−f(x)=∞,limx→9+f(x)=−∞,

Q: 1. For the function / whose graph is given, state the value of each quantity, if it exists. If it…

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Q: Q2: A particle move on the path has parabola shape with equationf(x) = a + bx + cx²; Find the…

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Q: Find the lim tan ( X-0

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Q: Calculate the following limit: lim X-0 -5.sin(x) 2.X

A: Given that a limit problem and we solve this problem by using general property of limit.

Q: Calculate (5.x+2)(sin(x)) dx The solution to any indefinite integral of the type given above will…

A: Explaination of the answer is as follows

Q: Find the value(s) of k such that the function is continuous at x = -1. (Enter your answers Sin (2x +…

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Q: Find dx dy by implicit differentiation. dx y cos(x) = 3x² + 4y² 11

A: consider the given function.

Q: Use the method of cylindrical shells to find the volume of the solid obtained by rotating the region…

A: The graph of bounded region

Q: According to one cosmological theory, there were equal amounts of the two uranium isotopes 235U and…

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Q: Differentiate the function. =="(x) = g(x) = 2 2 – 6x + 15 = = - 5

A: To differentiate the following function.

Q: 68-72. Higher-order derivatives Find f'(x), f"(x), and f""(x) for the following functions. 68. f(x)…

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Q: Find the derivative of the function. x x+5

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Q: 22. Show that (a X b) b = 0 for all vectors a and b in V₁.

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Q: Video Example < Sketch the graph of y = (x − 3)²(x + 1)³(x − 1) by finding its intercepts and its…

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Q: Evaluate the limit: - 7x - 21 lim x-3 x² - x - 12 =

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Q: Consider the following. y = Function g(x) = 1.5x + e* (0, 1) (a) Find an equation of the tangent…

A: Given: Function: Point: (a) To find an equation of the tangent line to the graph of the functionat…

Q: Question 1.22) (-4x+5k when x -1 find a value of k, if any, for which lim f(x) exist, and what is…

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Q: 8. The vertical asymptote of f(x) = x²+x-6 x²-x-2

A: The given function is; f(x)=(x2+x-6) /(x2-x-2) Find vertical asymptotes.

Q: How can I find the area of the region bounded by the given curves for y2 = x, y3 = x. The answer…

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Q: Let f(x) = b) lim a) lim f(x) = = x →∞ - 12x √√x +3 €118 f(x) = = Evaluate each limit:

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Q: The following table shows values of a periodic function f(x). The maximum value attained by the…

A: x024681012f(x)50-5050-5

Q: 10. A sandwich shop charges $7 for a foot-long sandwich with one protein and unlimited veggies. You…

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Q: Consider the following functions. f(x)=x-8, g(x) = x² Find (f+g)(x). (f+g)(x) = Find the domain of…

A: The given functions are  and

Q: Jse logarithmic differentiation to find the derivative of the function y = x+8 cos(x) 8x8

A: To find the derivative of the function using logarithmic differentiation

Q: Solve the problem. The total cost in dollars for a certain company to produce x empty jars to be…

A: C(x)=0.6x+23,000

Q: Find the solution to the initial-value problem Y y' + 7y= 2xe-8; y(0) = C.

A: The given differential equation is; y'+7y=2xe-8x, y(0)=C

Q: Find for each pair of functions. dy dt y = x2 - 2x, x = t? + 8 dy = 2

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Q: If f(x) is defined as follows, find (a) f(-2), (b) f(0), and (c) f(1). x² f(x) = -2 2x+4 if x 0 (a)…

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Q: A volume is described as follows: 1. the base is the region bounded by x = -y² +12y + 58 and x = y²…

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Q: ms Puzzles ab 3 4 14 2 Perimeter Magic Square Puzzle #2 1 1 3 You are given these 8 numbers: 42 4 3…

A: We can solve the problem only by trial and error method and there is no specific way to solve the…

Q: Find the derivative of the function. f(t) = 7t sin(πt) F'(t)

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Q: Find the horizontal and vertical asymptotes of the curve. You may want to use a graphing calculator…

A: y=5x2+x−1x2+x−6

Q: Example 6 Video Example) Find f'(x) if f(x) = In Solution Since f(x) = it follows that f'(x) =…

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Q: Q2: Find the absolute maximum and minimum of the function f(x, y) = x² + y² on the closed triangular…

A: To find absolute maximum and minimum?

Q: (1 + 2x²)e² dx

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Q: The region bounded by the given curves is rotated about the specified axis. Find the volume of the…

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Q: Q2: Find the absolute maximum and minimum of the function f(x, y) = x² + y² on the closed triangular…

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Q: (5) Given f(x) = 3ª, g(x) = log3 x, h(x) = 2-log3 (x-1), sketch their graphs on the same xy-plane.…

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Q: Find the lim (√9x² + x - 3x)

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Q: Find the derivative of the function. f(x) = x(4x - 7)³ f'(x) =

A: Since you have asked multiple questions. We will solve the first question for you. If you want any…

Q: Obtain the general solution to the equation. (x² +9) dy dx + xy-7x=0

A: Given

Q: 44. (a) Find all vectors v such that (1, 2, 1) X v = (3, 1,-5) (b) Explain why there is no vector v…

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Q: Find the moment about the x-axis of a wire of constant density that lies along the curve y = √3x…

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Q: Use Table 1 to find: (a) f(g(1)) (b) (d) g(ƒ(4)) (e) Table 1 1 f(x) 5 g(x) 6 X g(ƒ(1)) f(g(6)) 2 3 4…

A: Given

Q: f  f(x) + x2[f(x)]4 = 18 and f(1) = 2,  find  f '(1).

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