2. Use Calculus to find all local extrema of the function g(x)=x√3-x.

Q: Find the exact length of the curve. x = et t₁ y = 4et/2, 0≤t≤4

A: Given, .Formula for length of curve is,

Q: fe2x sin 3x dx

A:

Q: 1. Isolate X.8 (3 + x-4) 4 24+ T (3x + 1 8 = 3x + 1 2x-8 24-9 = X X = 15 T 8

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Q: find maximum rate of change of f(x,y)=x sin(y) @ the point (2,0)

A: To find the maximum rate of change of at the point .

Q: If a 4th order linear differential equation is such that the corresponding characteristic equation…

A: If a 4th-order linear differential equation is such that the corresponding characteristic equation…

Q: 2) Draw a direction field for the given differential equation. Based on the direction field,…

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Q: Determine whether C(A - B) is defined. If it is defined, express the result as a single matrix; if…

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Q: Use the factor theorem to determine if the given binomial is a factor of f(x). f(x)=x²-2x³ +5x²…

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Q: At what point on the curve x² - y² + x² = 0 is the tangent line vertical? (a) (0,0) only (b) (-1,0)…

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Q: A rectangle is inscribed in a semicircle of radius r = 16 as shown in the diagram below. 0 X y

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Q: x 2) f(x) = x² +1

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Q: Verify the identity + 1+cos 0 1-cos 0 2 + 2 cot²0

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Q: 6x Find the limits in a), b), and c) below for the function f(x) = - X-5 Use -∞ and ∞o when…

A: given limit to find

Q: 0 1 X g(x) g'(x) 2 1 3 When x = 7 then D 33 2 f(x) g(x) 25 -2 = 320 3 4 -1 0 -3 2

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Q: Visually estimate the location of the centroid of the region shown. Then find the exact coordinates…

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Q: Use the remainder theorem to determine if the given number c is a zero of the polynomial. f(x) = 5x²…

A: Remainder Theorem:If a polynomial p(x) is divided by the binomial x−a,the remainder obtained is…

Q: What values of a and b make the function f continuous everywhere? x² 4 a = f(x) = and b = - " X 2…

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Q: Find f(x) if y = f(x) satisfies dy dx 108yx¹7 and the y-intercept of the curve y = f(x) is 4. f(x) =

A:

Q: 1 8 Q1. Let f(x, y) = 3xy + / - 1. Т

A: f(x,y)=3xy+1x−8y

Q: 1. Consider the ellipse given by x(t) = 9 cost and y(t) = 81 sint for 0 ≤ t ≤ 2π (a) Make a sketch…

A: The given equation of  eillipse is for

Q: The line given by the parametric equations x= 3+2t, y=4-t, z=1 + 3t passes through the point (11, 8,…

A:

Q: 7. Given F(x)=√√√x+3 A. Find (fo (fog)(x) B. Find (9°F) (2) gof) → g (x) X -2 report domain and…

A: f(x)=sqrt(x+3)g(x)=x2-2.

Q: Use the nth-term test for divergence to show that the series is divergent, or state that the test is…

A: Consider the series

Q: Evaluate the integral. +C 2x + 9 x² + 6x +34 17 -da

A:

Q: Given f(x) = 2x³ - 12x² + 4x + 13 The possible inflection value is x = Concave Down interval is O…

A: The given function is

Q: Consider g(t) = 3t+ 6t² - 1 + 6t³+2+¹ Determine the intervals on which g is concave down. g is…

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Q: 1 · f(t) == t³-a¹t 5

A: f(t)=15t5−a4t

Q: Find the slope of the line tangent to the graph of the function at the given value of x. == -√x; x =…

A:

Q: (a) Find parametric equations for the line segment that joins the point P(2, 3, -3) to the point…

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Q: For the given double integral, sketch the region of integration and write an equivalent double…

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Q: Find the volume of the region under the surface z = xy² and above the area bounded by x = y² and x +…

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Q: Simplify: x5/6y2/7x4/34/7 x2/3y1/7 Entry Tip: put the numerator and denominator in parenthesis. Also…

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Q: The answers are K=73.333 and L=146.67 Ibs, can you explain to me how to get there?

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Q: Given f(x) = 21x¹ - 26x³ - 120x² +7x+4 The possible inflection values are x = O Concave Down…

A: In this question, we will find the concave down and up intervals.

Q: Roberto has plans to build a tree house in his backyard. He takes measurements from the ground and…

A: Here,

Q: Which of the following is/are signified by lim f(x) = ∞? x→a The limit exists and equals infinity.…

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Q: A rectangle is inscribed in a semicircle of radius r = 16 as shown in the diagram below. x The area…

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Q: dy dx - 5ln(t), y = 4t² - 4t-2

A:

Q: Find d'y if (x)=3x³ (√x-2). d³y dx³

A: To find Note: Since the student has posted multiple questions and does not mention any specific…

Q: Use logarithmic differentiation to find the derivative of the function. y = (tan x)8/x 11

A:

Q: differentiate. do not simplify f(y) = (3-y^3)^3/4

A: given function

Q: Differentiate the following: a) y=-x²+x-5 (b) y = 10 + 2 3 (c) y = 2√x - X

A: According to Bartleby guidelines we are supposed to do the first three sub parts of multiple sub…

Q: Let 16x-5 1x² +5 Enter the exact value of the one-sided limit lim f(x) 3-2 f(x) = if x ≤ 2 if x > 2

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Q: Verify that f(x) = 2x^3 + x^2 − x − 1 satisifies the hypotheses of the Mean Value Theorem on the…

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Q: Evaluate the following integral using integration by parts. Se 10x cos x dx

A: I=∫e10xcos⁡xdx

Q: When a circular plate of metal is heated in an oven, its radius increases at a rate of 0.01 cm/min.…

A: Radius = 60cmdr/dt = 0.01 cm/min.

Q: The radius r of a circle is increasing at a rate of 3 inches per minute. Find the rate of change of…

A: Please solve the given problem using the concept of derivatives.

Q: Which step is part of finding the derivative of the function below? The correct choice may not be in…

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Q: Evaluate the indefinite integral S 16 (49 - x2) 19/2 dx

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Q: Find aw/as and aw/ât using the appropriate Chain Rule. Values Function w = y³ - 2x²y x = es, y =et S…

A: