Evaluate the integral. [²8+ ¹8+u² u³ 3 - + log (2) du

Q: Suppose f(t) = 5t² + t + 3. Evaluate: lim f(t) = t→-2

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Q: The solution of the D.E. y√√1-x² dy + x√1 – y² dx = 0 is

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Q: Suppose that a particle moves along a straight line with acceleration defined by a(t) = t - 5/2 in…

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Q: Re-write the following exponential equation in logarithmic form. 11 3 b = Is equivalent to: log, (x)…

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Q: Find the domain and range of y = log7(4 + 3x) + 12.

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Q: K Determine the horizontal asymptote of the function. If none exists, state that fact. 2x+3x³-6 5x°…

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Q: 8. Represent 1/7 with Egyptian symbols 9. Write as a sum of unit fractions: 3/8

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Q: Find the arclength of the curve x = 20t 8, y = 21t + 4 with 2 ≤ t ≤ 9.

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Q: For the following function f, find the antiderivative F that satisfies the given condition. f(v) = s…

A: Introduction: A function whose derivative is f is said to be an anti-derivative of f. In other…

Q: Two variable quantities A and B are found to be related by the equation given below. What is the…

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Q: Eliminate the parameter t to find a simplified Cartesian equation of the form y = mx + b for ſ x(t)…

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Q: Let F(t) = < -1² + 5, t4 + t, In a. Determine the coordinates of the point on the curve traced out…

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Q: (b) Parametric equations: Rectangular equation: Parametric equations: y=2 sint X || y= 0 11/13x + 4…

A: Ques (a) Rectangular equation: x2+y2=4x2+2sint2=4x2=4-4sin2tx2=41-sin2tx=41-sin2tx=4(cos2tx=2cos(t)…

Q: Evaluate. 5 -1 -1 (4x²-3x+5) dx (4x²-3x+5) dx = (Type an exact answer in simplified form.) ***

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Q: Given the function: a. Find f'(x) and f"(x) b. Determine the following properties of the graph of f.…

A: Please see the below picture for detailed solution.

Q: Solve the differential equation. FD dy dx 3e * y = 2, x > 0

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Q: If f f(x) dx = 6, f f(x) dx = 2, and f, g(x) = -5, find f₁[2f(x) — 4g(x)]dx.

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Q: 4) The population of a city doubled in 30 years. What is the exponential growth rate?

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Q: The continuous function g is decreasing for all x. Selected values of g are given in the table,…

A: The function g is decreasing and the given values are, x b b2 4b 6b 8b gx 12 9 5 3 -2 We…

Q: ind an equation of the tangent plane to the surface z² y + In(2y — z) at the point (1,1,1). X

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Q: Question Convert the equation r = 6 cos(0) + 3 sin() into an equation in rectangular coordinates.…

A: in polar coordinates   x=rcosθ   and  y=rsinθr2=x2+y2given  r=6cosθ+3sinθ

Q: 1) Find the general antiderivative of the function y = O 0.1Ln/x^3+x) + C O 10Ln|x^3+x| + C…

A: Given query is to find the integral.

Q: Find lim_ (x+3)² x→-5

A: Given: limx→-5x+32

Q: Evaluate the integral. ['w² w² In(w) dw

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Q: 6. Use the method of Lagrange multipliers to find the points on the Sphere are closest to x² + y² +…

A: Given equation of sphere x2+y2+z2=36 let  any arbitrary point on sphere is  (x,y,z) now distance…

Q: Use the given information to find the exact value of each of the following. a. sin 20 b. cos 20 c.…

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Q: b) Find a function f(x) such that both f′(x) = cos(x) + e^2x + 2x and the tangent line to f(x) at x…

A: Let's find function f(x).

Q: 1) 2² Evaluate ze x² + y² + 2 dv where E is the portion of the ball x² + y² + z² = 1 that is in the…

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Q: Suppose that a particle moves along a straight line with a velocity v(t) = 4 - 2t, where t is in the…

A: NOTE: Refresh your page if you can't see any equations. . the given velocity function is  and the…

Q: Sketch the region enclosed by the given curves. Decide whether to integrate with respect to x or y.…

A: Here is the solution:

Q: If f(x)=(², what is f'(-1)? (Note: Round your answer to the nearest integer.)

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Q: The point of intersection between these two lines 2x + y = 4 x + 3y = 7  is  ....

A: Given the equations are  2x+y = 4 ......... (1)  X+3y = 7 ...........(2) Multiply the equation (2) *…

Q: Suppose Evaluate each of the following limits: (a) (c) lim f(x) = -3, x-a lim f(x)]² lim /h(x) x-a…

A: given  limx→af(x)=-3limx→ag(x)=0 and limx→ah(x)=8accorging to bartleby guide line we do only first…

Q: Evaluate. 2 √2x dx

A: Our Aim is to evaluate the integral given below:-∫022x dx -(i)

Q: 11. Suppose the population of a town is 23,000 people in 2010. Write an equation for the population…

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Q: On which open intervals is the function f(x) upward? -2x decreasing and concave

A: Please see the below picture for detailed solution.

Q: answer Choice if the limit exists. 1. limit 2. limit 3. limit = 2 4. limit 0 5. limit does not exist…

A: Given   limx→1f(x)   When   f(x) = 3x2-1, when  x≠1        = 3   , when x = 1

Q: 2. xy + y = (xy) ³/nx

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Q: r(t) = m with -∞ < t <∞

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Q: Question Using Desmos, plot the point -1, 5TT 3 in the polar plane.

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Q: The graph of a function g is given. 1 = 0 Consider the integral I when answering the following…

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Q: K A soda can manufacturer wants to minimize the cost of the aluminum used to make their can. The can…

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Q: Determine the domain of the function of two variables. g(x,y)= 8 y+x² {(x,y) y*)

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Q: 4).    Find the Taylor polynomial of degree two approximating the given function centered at the…

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

Q: The solution of the D.E. xdy - ydx = x² + y²dx is 2 a. y-√√x² + y² = cx² O (a). c. y+√√x² + y² + cx²…

A: Given: xdy-ydx=x2+y2dx

Q: Substition Simple Ing (x + Iny) dx = (x²) dy-0 III Solve using

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Q: Classify the following as a linear relationship, exponential relationship, or neither. Explain your…

A: We need to determine relation.

Q: Find a formula for the general term an of the sequence assuming the pattern of the first few terms…

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Q: Find all possible functions with the given derivative. t 1²/24 f'(t) = cos 9t- sin f(t) =

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Q: Identify the equation of each of the following graphs. W 7/2 37/2 7.

A: Since you have asked multiple question, we will solve the first question for you as per our guide…