To algebraically find the points of inflection of f, we find values of p in the domain of f such that f"(p) is O or undefined and ... O Look to see where f">0 O Look to see where f"<0 O then p is a point of inflection and no further test is needed O determine the signs of f" around p to see if f changes concavity at p

Q: Find the numbers b such that the average value of f(x) = 3 + 8x − 6x2 on the interval [0, b] is…

A: formula for average value is  favg=1b-a∫abf(x)dx∫xndx=xn+1n+1+c

Q: a(t) = t2 −4t + 6 , s(0) = 0 , s(1) = 20

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Q: Use part one of the fundamental theorem of calculus to find the derivative of the function. =…

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Q: [ sin(lnx) x dx

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Q: Calculate the derivatives of: a. y=bx² b. The above at f(4) C. Y=-2x²

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Q: Determine the area of the region bounded by y = (x-4)e5x² - - 40x and y = 0 on the interval [0,8].…

A: NOTE: Refresh your page if you can't see any equations. . given functions are and the given…

Q: Assume that the radius r of a sphere is expanding at a rate of 7 in/min. The volume of a sphere is V…

A: Differentiate volume wrt t then put value

Q: Find the vertex, focus, and directrix of the parabola x² +12y = 0.

A: The given equation is x2+12y=0

Q: Use the Ratio Test to determine whether the series is convergent or divergent. Identify an n+1 00 Σ…

A: NOTE: Refresh your page if you can't see any equations. . here the sequence is

Q: Given the graph of the function f(x) below, use a left Riemann sum with 4 rectangles to approximate…

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Q: The graph of the equation y = x²+x-2 meets: Othe x-axis at (-2, 0), (-1,0), and the y-axis at (0, 2)…

A: for x-intercept put y=0for y-intercept put x=0y=x2+x-2

Q: Use the fundamental identities and simplify the expression sin² x (cot² x + 1) to get a numerical…

A: Given sin2xcot2x+1

Q: Find the exact length of the polar curve r = = 2cos 0, 0≤ 0 ≤ π.

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Q: 3. Find the inverse function f-¹(x) of f(x)=3 sin 2x

A: The given function is: fx=3sin2x   To calculate the inverse function of the given function…

Q: 15) y = sec ²(x); dy = ? Jx B) 2 secx. tanx c) 2 sec²³x. Tanx E) TanX A) 2 SecX D) Sec²x. Tan²x

A: Given query is to find the derivative.

Q: Find all the antiderivatives of the function f(x) = -6.

A: ∫xndx=xn+1n+1+cgiven  f(x)=-6

Q: I m 9 = (⁹ε- ¹ 1/2-) ƒ = = (1 ¹4²)

A: To find the value of function at given points.

Q: Analyze and sketch a graph of the function. Find any intercepts, relative extrema, points of…

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Q: Hello, Please show all your and solve the following the

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Q: Find the area of the shaded region. 30) f(x) = -x3 + x² + 16x g(x) = 4x -4 (-3,-12) -2 30- 20- 10…

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Q: Question Find the equation of the tangent line to the curve defined by the equations = ₁y = 1/2+1…

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Q: Evaluate each of the following integrals 2. √2x²-x+4 dx S x(x²+4)

A: Given integral ∫2x2 - x + 4x ( x2 + 4)dx

Q: The acceleration (in m/s²) of a particle moving along a line at time t (in seconds) is given by -2t…

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Q: Find the domain and range of g(x)= In(tanx) on [0,1]. Show some work or explanation.

A: The given function gx=lntan x on 0, π. We have to find its domain and range.

Q: Find the area of the region of r= √2 + sin(theta) and r= 3sin(theta)

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Q: An aircraft factory manufactures airplane engines. The unit cost C (the cost in dollars to make each…

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Q: f(x)=(3x2−12)2 Step 2 of 2:  Use the Second Derivative Test to locate any local maximum or minimum…

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Q: Determine the length of the curve Cost 10204 TI 4 4

A: To determine the arc length of the polar curve

Q: Find a plane containing the point (2,5,-5) and the line of intersection of the planes 5x and - 2x -…

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Q: Let A be the area of a circle with radius r. If dr dA dt when r = 5. dt = 3, find

A: Given A = Area of the circle r = radius of the circle drdt = 3 r = 5 dAdt = ?

Q: Sec² (x); dy = ? 15) y = Sec²(X) ; Jx A) 2 SecX B) 2 secx. Tanx D) Sec²x. Tan²x c) 2 secx. tanx E)…

A: NOTE: Refresh your page if you can't see any equations. . take derivative

Q: Z = e¯(4x²+3y²) at point (0, 0, 1).

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Q: If f(x) = sin(x³), find f'(x) Find f'(5)

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Q: Let R be the region bounded by the parabolas y = 2x² + 5x-3 and y = x² + 4x - 1. a. Find the…

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Q: 4. y = 2³, y = x

A: find intersection points graph

Q: Solve the differential equation with initial condition. y + y = 0, y(0) = 4

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Q: not correct

A: Let's solve triple integral.

Q: (14) y = Tan¹ (3); dy =? ax A) 15) 4+x² E) y= B) - 2√4-X² x²+4 Sec²(X); dy = ? Jx Tanx √4x² D) +…

A: To solve the problem we use derivatives properties and trigonometric properties.

Q: A 20 ft ladder leans against a wall. The bottom of the ladder is 5 ft from the wall at time t = 0…

A: NOTE: Refresh your page if you can't see any equations. .

Q: The graph of the equation x² - 2x + y² +6y-6=0 is: a) a line through the point (2,-1) b) a parabola…

A: Given equation:- x2-2x+y2+6y-6=0

Q: Let f(x) = ln(x5) ƒ'(x) = ƒ' (e³) =

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Q: Evaluate. (Be s (In x 20 X (In x)20 dx X (Type an exac=

A: NOTE: Refresh your page if you can't see any equations. . ...............(1) substitute…

Q: Obtain x²dx by integration.

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

Q: Integrate the indefinite integral. Se-2 da

A: ∫eaxdx=eaxa+c

Q: properties of natural logarithms to simply the function. f(x)=ln(5x)-ln(5)

A: Given query is to simplify the expression.

Q: Use part one of the fundamental theorem of calculus to find the derivative of the function. [Hint:…

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Q: Solve for y:  3log10(y)=-6

A: NOTE: Refresh your page if you can't see any equations. . divide both sides by 3

Q: Use the product rule to find the derivative of f(x) = ( − 4x¹⁰ – 2x³) (9eª + 6) Use e^x for e. You…

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Q: Use the Ratio Test to determine whether the series is convergent or divergent. Σ COS (2) n = 1 n!…

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Q: Find the minimum and maximum values of z= 5x + 6y, if possible, for the following set of constr…

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