Consider the following. Find f'(x). f'(x) = f(x) = 48x 4x² X = - Find the critical numbers of f(x). (Enter your answers as a comma-separated list. If an answer does not exist, enter DNE.)

Q: Consider the indefinite integral ax + b + where Then the integrand decomposes into the form C d a =…

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Q: 5+ 4 3 2 1 -1 -2 -3 -4 -5+ 1 8 + 7 6 5 4 3 2 1 -1 -2 -3 3 -5 -6 -7 -8+ 4 The graph of a function y =…

A: The graph of a function  is shown. To make a sketch of theantiderivative F, given that F is…

Q: For the sequence defined by: a1 = 2 an+1 = Find: a2 a3 a4 = 4 an - 3

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Q: Let g(z) = 6 Determine the most general indefinite integral of g. 1 6dz

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Q: Find the volume of the solid generated when the shaded area is revolved about y = -1. y y = 2x y=x²…

A: To find the volume of the solid generated when the shaded area is revolved about .

Q: Find the complete solution of the linear system, or show that it is inconsistent.

A: A system of equations is inconsistent when it has no solution.that is no real numbers as variable…

Q: Find the general solution of the homogenous differential equation 9y" - 30y' + 25y = 0.

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Q: Gilbert Strang video 'Min, Max and Second Derivative,

A: The objective of the question is to understand the concepts of minimum, maximum and second…

Q: 15. An open rectangular box is to be made by cutting equal-sized squares from the corners of an 8"…

A: The dimensions of the box are:Length: L=15-2xWidth: W=8-2xHeight: H=x

Q: k. y = ln x 1. m. y = y = 5 cos x + 8 lnx + 3x³ 3x¹+3x²+1 x

A: Given: y= ln(x)Solution: y= ln(x)Differentiating y with respect to x we have dydx= ddx(ln(x)) ⇒y′=1x

Q: Find the second derivative of the following functions: a. f(x) = x5 + sin x b. f(x) = x² + == x c.…

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Q: Suppose g is a function which has continuous derivatives, and that g(0) and g"" (0) = 18. What is…

A: Suppose  is a function with continuous derivatives, and that .To find the Taylor polynomial of…

Q: Evaluate the given definite integral. 3 [(-8 -4 (-8z - 7)dz =

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Q: Find the sum of the series: n=0 (-1)"49"+2 n!

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Q: The system of first order differential equations y₁ = 5y₁ + 1y2 y₂ = −4y₁ + 1y2 where y₁ (0)= 4, y2…

A: The objective of the question is to verify if the given functions y1(t) = (4 - t)e^(3t) and y2(t) =…

Q: Click on the graph to view a larger graph Use the Law of Sines to find the indicated side a given in…

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Q: Evaluate the given definite integral. [²e" 7 e" du t

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Q: Find the Derivative and the Line Tangent to a Curve at a Point. 2 (-2x - 3)² Given that R(x) R'(x)…

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Q: S 12x+8 3x²+4x+8 dx

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Q: The function y(x) saifies the following equation: Find an expression for dy dx 5 x² − 2xy+3y² − 3 x…

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Q: The graph of f(w) = 9 is given below. 10- 8 6 5 4 -4-3 -2 -1 3 1 2 3 4 5 6 7 8 9 Determine the…

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Q: Evaluate the integral: O x ○ x = 3 sec (0) 0x = 8 sin(0) (A) Which trig substitution is correct for…

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Q: Breathing is cyclic and a full respiratory cycle from the beginning of inhalation (t =0) to the end…

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Q: A stone is dropped from the upper observation deck of a tower, 500 m above the ground. (Assume g =…

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Q: A tall pipe is 30 feet tall. A person with a height of 6 feet walks away from the pipe along a…

A: The objective of this question is to find the rate at which the person is moving away from the pipe.…

Q: To check for the result, you have to prove that + C] = 8⁹. + sec²0. d 1 10 de Evaluate the left side…

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Q: Given the geometric sequence: 20 3 find a formula for the n-th term: ao = 2, a₁ a1 = , a2 = 200 9…

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Q: Evaluate the following definite integral. π JU OA. (( sin 8t)i + (cos 8t)j + (10t)k) dt Select the…

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Q: Starting with an initial value of P(0) = 50, the population of a prairie dog community grows at a…

A: The growth rate of population of prairie dog community is P(0)=50

Q: M8 ηχη n=1 3"

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Q: Evaluate the limit lim x →0 O -1 1 18 1 9 √81-x-9 X

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Q: r = sin(20), r = cos(20)

A: Given that the polar curve

Q: A physician invests $24,000 in two bonds. If one bond yields 6% and the other yields 12%, how much…

A: Given that a physician invests 24000 dollars in two bonds , 6% and 12% , total annual income 1980…

Q: 5. Use Part one of the fundamental theorem of calculus to find the derivative of the following…

A: Since you have asked multiple questions in a single request so we will be answering only first…

Q: Find a power series representation for the function. f(y)=In f(x)= In[11+y)

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Q: Consider the following position function. a. Find the velocity and speed of the object. b. Find the…

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Q: g. y = tan x h. y = t+√√2t+√1-5t

A: To find the derivative of the following functions.

Q: Find the limit of f(x) = lim f(x) = -5 9√x+x 3x-9 X→∞ (Simplify your answer.) as x approaches co.

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Q: S dx x+7 2x-3

A: To solve the following integral.

Q: The figure below shows the derivative F'. If F (0) = 15, give (x, y)-coordinates of all local maxima…

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Q: = (a) The fourth Taylor polynomial for f(x) = ln (sec(x)) at a co + c₁x + ₂x² + 3x³ + ₁x² where Co =…

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Q: 9. Let f(x) = sinx, g(x) = cos x. The functions f and g, considered on the interval 0, π], are…

A: Given that the function are

Q: Find an equation of the line tangent to the curve at the point corresponding to the given value of…

A: Given,

Q: Find the indefinite integral and check the results by differentiation S(4x²+ + 3)²dx

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Q: The curve r(t)= (f(t),g(t)), where f and g are twice differentiable, has f'g'"-f"'g' curvature…

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Q: Let g(x) = 6e* Determine the most general antiderivative of g. [6e²dx = [

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Q: 2) Find S -18 dx

A: The given integral is e1/x.

Q: A= B n ed Use the right triangle and the given information to solve the triangle. a=1, c= 8; find b,…

A: Given,

Q: For what value of a is the following function continuous at every x? f(x) = x²-30, x<10 x≥ 10 ax,…

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Q: 4. Find the function given by the power series n f(x) = Σ + ²)", x+2 when -7 < x < 3. 5 n=1/

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