1. Let g(x) = ln ((f(x))² + x). Determine g'(5) if f(5) = 2 and f'(5) = 3.

Q: According to a study, a vehicle's fuel economy, in miles per gallon (mpg), decreases rapidly for…

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Q: Find dy dx xy + y² = 5 dy-0

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Q: Prove that for all integers n, it is the case that n is even if and only if 3n is even. That is,…

A: We have to prove that for all integras n, it is the case that n is even if and only if 3n is even.…

Q: Find the center, foci, vertices, asymptotes, and radius, as appropriate, of the conic section 2x² -…

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Q: 5. Graph the following in polar coordinates (a) rsin = -3 (b) # = 5π 6 (c) 1<r<4

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Q: 2. For the function f(x) defined by the graph below, with each mark representing one unit, evaluate…

A: The objective of the question is to evaluate the limiting value ( functional value) of the given…

Q: 5. Solve the second-order equation xy" +2y' = 12x² by making the substitution u=y'..

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Q: Find all relative extrema of the function. Use the second derivative test where applicable. (If an…

A: The given function is

Q: Find the angle between u and v in radians. Round to the nearest hundredth of a radian.u=-4i-7j,…

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Q: Change the order of integration. S J f(x, y) dy dx

A: given

Q: Find the values of the other trigonometric functions given the following conditions.  a. sin theta =…

A: Find the values of the other trigonometric functions given the following conditions. a. sin theta =…

Q: Find the directional derivative of f(x, y) = sin(x + 2y) at the point (5, 5) in the direction = 3/4…

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Q: = OF MATHEMATICAL INDUCTION 2 (3") + 1 15 DIVISIBLE BY positive integer F E E

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Q: Let f(x) = x². There are two lines with positive slope that are tangent to the parabola and that…

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Q: Find the derivative of the function at P0 in the direction of u. f(x,y)=4x2+3y, P0(7,10), u=3i-4j

A: f(x,y)=4x2+3y, P0(7,10), u=3i-4j

Q: Find the partial derivatives of the function B || || w = √3r² +8s² + 6t²

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Q: Find the exact length of the curve. 36y² = (x² - 4)³, 2≤x≤6, y 20

A: Find the exact length of the curve.36y2=(x2−4)3,2≤x≤6,y≥0

Q: 6. Identify the key points and coordinates (center, vertices, covertices, foci, transverse axis and…

A: The given equation of hyperbola is

Q: 2 y³ 4. Solve y' +-y X X² = using the following technique: A Bernoulli differential equation (named…

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Q: Find the first partial derivatives of the following function. f(x,y) = 3xy³ + 1 =

A: By treating one variable at a time and other as a constant, we can find the partial derivative.

Q: ㅐㅍ 3 1/2 S (2+4C05(0)) ² do 2 싫어

A: To evaluate the following integral.

Q: Find the length of the indicated portion of the curve by first finding the arc length parameter…

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Q: Ihd an equation of the line tangent to the curve y = An equation of the tangent line is 5x 2 x +4 at…

A: Here we will solve it on finding the slope at x=4 after that we will use the formula of equation of…

Q: Give the Taylor series for sin x about xo = 2

A: To give the Taylor series for .

Q: Compute the Taylor polynomial of degree 4 for g(x)=cos x centered at x=0.

A: To compute the Taylor polynomial of degree 4 for  centered at .

Q: The function g(x) is defined by the rule 9(x)=(-X). If the point (12, 12) is on the graph of the…

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Q: Find the derivative of the function. g(x) = sec¯¹(8e*) g'(x) = X

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Q: Find the GCF of the expressions. 12x¹4yz6, 24x6z8, and 4xyz7

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Q: ex - 32 √x +x 22

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Q: Let G=7f-g, where the graphs of f and g are shown in the figure to the right. Find the following…

A: G=7f-g

Q: = (a) Draw the exponential function: y 3x Also identify the asymptote to this function in your…

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Q: 2. General Change to Standard Form (Ax+By = C form) 2 y + 4 = = (x − 8)

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Q: Find the volume of the given solid. Enclosed by the paraboloid Z = 5x2 + 4y2 and the planes x = 0, y…

A: The region enclosed by planes

Q: For the graph of a function y = f(x) shown to the right, find the absolute maximum and the absolute…

A: Using the given graph we can identify all the local and absolute extreme points

Q: Write a polynomial f(x) that satisfies the given conditions. Polynomial of lowest degree with zeros…

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Q: For the polynomial, determine its standard form, degree, coefficients, leading coefficient, and…

A: Given:- 5x + x4 - 3Standard Form is given by Standard form :- x4 + 5x - 3

Q: 6. A fisheries biologist is stocking fish in a lake. She knows that when there are n fish per unit…

A: The average weight of each fish is:Number of the fish is n

Q: Set up the definite integral required to find the area of the region between the graph of y = 16 -…

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Q: If a rock is thrown vertically upward from the surface of Mars with velocity of 15 m/s, its height…

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Q: 2. §11.3. Q52. Let w = √x² + 4y² - 2². Find (a). Əw/dx|(2,1,-1); (b). Ow/dyl (2,1,-1); (c). Ow/Oz…

A: The given function .The objective is to find the following,(a) (b) (c) .

Q: Determine the derivative with respect to a: In (255)

A: Given, .We know,

Q: ind  dy/dx  by implicit differentiation. x4(x + y) = y2(5x − y)

A: The given equation is

Q: 2) Determine whether the sequence is convergent or divergent. If it is convergent, find its limit…

A: To determine whether the sequence is convergent or divergent. If it is convergent, then to find its…

Q: 4. The position function of a particle is s = t5 - 60t³, t > 0, where s is measured in meters and t…

A: Given, .

Q: Suppose that the number P(t) of bacteria in a culture after t days is given by the formula P(t)=76…

A: Suppose that the number  of bacteria in a culture after t days isgiven by the formula, To determine…

Q: Suppose that a forest fire starts at point P and spreads in every direction at a speed of 30…

A: Suppose that a forest fire starts at point P and spreads in every direction at a speed of 30…

Q: Find the first partial derivatives of f(x, y) = 9x³y° + 6x³y² +2. af ax ||

A: Given, .Formula of partial derivatives:

Q: Simplify the expression. (16x 16x²x) (- 8z4 28x²z³ 14y²

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Q: A new music company wants to start selling col л(p) 100p-2.5p², where p is the price of a collection…

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Q: The function s(t) describes the motion of a particle along a line. s(t) = 35² + 3t - 210 (a) Find…

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