Problem 3.4: Use Rationalization to Evaluate a Limit Algebraically Evaluate the following limit: aja lim x →4 3x²-8x x-4 1 4

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A: We have to find the delta using the epsilon-delta definition of a limit.

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A: The blanks are filled in step 2. And answers to a and b are given in solution

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Q: Use the given graph to estimate the value of each derivative. (a) f(-3) (b) f(-2) y=f(x) 1 1 X

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A: Here we will use the definition of continuity to solve this and we will find the value of x,

Q: √(-1-x); (4) Let g(x) = { x²; 3x - 5; if x 2. A (c) State the domain and range

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A: The given integral is x2)

Q: EXAMPLE 5 Video Example Where is the function f(x)=(x) differentiable? SOLUTION If x > 0, then [x]-…

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

A: To find the limit .Then by using the  definition to prove that the limit is .

Q: L³ 1 (6 - 5x) dx

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A: Given:Initial capitalization, A(0) = $5 billionRate = 20% Time taken = 5 yearsSince, the…

Q: 1. y = 1/x3/2, x = 4, the x-axis to the right of x = 4.  2. y = 1/(x + 1)3/2, the coordinate axes,…

A: (1) y=1x3/2,x=4, the x -axis to the right of x=4

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Q: Find the critical point(s) of the function f(x, y) = 3x¹ + 3y¹ – xy. The critical point that lies in…

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Q: Find the average value have of the function h on the given interval. In(u) u have = h(u) = [1, 5]

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Q: During a recession a firm's revenue declines continu- ously so that the revenue, R (measured in…

A: Given that       During a recession a firm's revenue declines continuously so that the revenue,…

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: EXAMPLE 7 Video Example A manufacturer produces bolts of a fabric with a fixed width. The cost of…

A: To find-(a) What is the meaning of the derivative f '(x)? What are its units?  (b) In practical…

Q: √3/² sin cos de u = sin 0 du = cos Ꮎ de π/2 = & */²* sinº 0 cos 0 db = π/2 = 6t1² 2² [ u6. du /2 -…

A: The given integral is sin6(theta) cos(theta), limit from 0 to pi/2.

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Q: 7. Let Evaluate each of the following, if it exists. a. lim f(x) x-1 b. C. lim f(x) f(x) = f(1) X,…

A: The given function,The aim is to find the following limits,(a) (b) (c) Note: Since you have posted a…

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Q: 6 201 8 xif In this problem, we'll use the TI-84 graphing calculator or Desmos to graph f(x) and its…

A: The Given piecewise function is we need to graph the function f(x).

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A: We have to fill in the blanks from the given information.

Q: Use logarithmic differentiation to find the derivative of the function. y=(√x)³x y'(x) =

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A: Application of algebra

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Q: Find the solution of with y(0) = 9 and y'(0) = 7. Y y" + 3y = 126 sin(3t) + 162 cos(3t)

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Q: Find a particular solution to the differential equation y" + 3y' - 4y = 32t³.

A: As the degree is 3 , particular solution can be given as below :

Q: (3) Let R(x) = 2 +3- (c) Evaluate the function when x = -6, -5, -4.5, -3, -0.5, 1.5, 4, 6;

A: To evaluate the function at given values of x

Q: Let F(x, y, z) = (6e* sin(y))i + (6e* cos(y))j + 7z²k. Evaluate the integral F · ds, where c(t) =…

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Q: Differentiate the function. 7 +7 11 y = Sex q

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Q: Find the average rate of change of the function f(x), given below, from x = 1 to x = t. f(x) = x² −…

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Q: Suppose the derivative of a function fis f'(x) = (x + 2)²(x-4)³(x − 6). On what interval is…

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Q: Find the average value fave of the function f on the given interval. x² (+3 (x³ + 9)² f(x): = [-1,…

A: Find the average value fave  of the function f on the given interval.f(x)=x2(x3+9)2,[−1,1]

Q: In an object was thrown upward at 64 ft/s from a height of 20 feet, its height h after t seconds is…

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Q: and give EXACT answer (no decimals). (a) lim 0–૫ 1 2h+3 (b) lim x-2 h 1 3 Find the limit…

A: The given limits,(a) (b) The aim is to find the limits.

Q: Q1: A: Find the maximum and minimum, if any, of the function f(x) = 4x³ - 18x² +27x-7

A: The given function

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Q: Find the acute angle (in degrees) between the planes 2x + 5y2z = 4 and 2x + 2y - z = 1.

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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: f(x) = X √16 + 3x - 4

A: L=limx→0x16+3x−4

Q: Let f(x) = log21 (10x + 60) - 15√√x.

A: f(x)=log21⁡(10x+60)−15x

Q: 3. a. b. As a snowball melts, its surface area and volume decrease. The surface area, S, in square…

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Q: Find the limit: √2x + 30-6 x+3x²8x + 15 lim ||

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