Given that f(x) x = -1 WA = X x + 1 and f'(x) = 1 (x+1)²' determine the critical numbe

Q: ate ſ- dx 4x²+1

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Q: E A4 sin (e-² + ln z) + C 4 sin (-e-²) + C B O A § 4 (½ − e¯²) cos (e¯² + Inz) dz B E None of the…

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Q: lim x →∞ (bx+a)²(ax+b)² (ax²+bx+1)²

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Q: The limit lim (x,y)→(4,-5) exists and equals to Select one: O True O False 25x²-16y² -5x-4y -40

A: Given the limit is  limx, y→4,-5 25x2-16y2-5x-4y.

Q: A road perpendicular to a highway leads to a farmhouse located a = 1.5 km away. An automobile…

A: This question is based on application of derivative.

Q: True or False: To evaluate the integral [si we save one sine factor and use sin²x = 1 - cos²x to…

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Q: π sin" g 2. So cos² g dg

A: The given integral is;  Sin5g/Cos2g, limit from 0 to pi.

Q: Use the Laplace transform to solve the given initial-value problem. y' + y = 8(t-1), y(0) = 8 y(t) =…

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

Q: 1 Give the antiderivatives of X The antiderivatives of 1 2 are

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Q: graph off consists of line segments and a semicircle, as shown in the figure. Evaluate each definit…

A: According to bartleby guidelines, we are supposed to do only first 3 subparts. If you want more to…

Q: 8. Use the graph of the function f to find the following: 13 (-5,0) 4 -3 -2 -1 (-3,-2) 3 2 H (-1,-2)…

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Q: 1. Find the domain of the vector function r(t) =

A: 1. Given Vector Function,rt = lnt+2, t1-t2, 2tt2 -4

Q: π S xsin xdx

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Q: Use the method of undetermined coefficients to solve the initial value problem. 33 y ==cos2t 10 33…

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Q: 1. Determine whether the resulting series when x = -4 absolutely converges, conditionally converges,…

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Q: Evaluate the following integral: sin²(a) da

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Q: Let f(x) = x³ + √√. Then f'(1) = 02 O 1.5 O 3.5 04

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Q: Let f(x) = 2x - 13. Determine f-1¹(x).

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Q: and x = = z = e-22 In (2-y), Select one: O True O False - 6t, y = t-s, then the value of 3 is equal…

A: In this question we have to find whether the given statement is True of False.z=e-2x…

Q: y-values 9: 8 7 6- 5 4 3- 2- 1 g(x) f'(1) = 1 If f(x) = g(h(x)), then --1/32 2 3 x-values Submit…

A: 1st We have to extract equation from given graph. Then we have to apply according to question asked.…

Q: Find the derivative of the function y = arctan x + x 1+x²

A: Given: y=arctanx+x1+x2Recall the formulas:ddxarctanx=11+x2     ..........1ddxuv=vdudx-udvdxv2…

Q: Question 32 Find the average rate of change for the function) f(x) = x² + 7x from 1 to 4. 12 desmos…

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Q: Find the angle between the vectors in radians and in degrees. (Round your answer for part (a) to…

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Q: If limx-5 f(x) = 4, limx-5 g(x) = 2, and limx-5 h(x) = 18, what is the value of lim x-5 4f(x) + g(x)…

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Q: The function ³ - 3x² has a point of inflection at x = 2 x = -2 Ox=0 O x = 1

A: Let the function,   f(x)=x3-3x2

Q: Find a parametrization r(t,s) for the plane which contains the point P(-9, 7, 1) and the line…

A: Use plane concept

Q: The radius of a sphere is decreasing at a rate of 1/4 cm/s. At what rate is the volume decreasing if…

A: The radius of a sphere is decreasing at a rate of 14cm/s.The radius is 2cm.

Q: rate of 10 cubic feet per minute. It forms a pile in the shape of a right circular cone whose base…

A: Given,       Gravel is being dumped from a conveyor belt at a rate of 10 cubic feet per minute. It…

Q: Question 21 The slope of the tangent line to the curve at the point where x = = is 00 O DNE O +1 0-1…

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Q: π/2 0 /1-cos2xdx

A: solution:-∫0π21-cos2xdxwe know that cos2x-sin2x=cos2x1-sin2x-sin2x=cos2x1-cos2x=2sin2x

Q: A) f(-1)-f(-2) (-1)-(-2) QIn parts (A)-(C), find the indicated quantity for y=f(x)=4-x². = N

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Q: If y = x?, then dy = a Ο 2 Δε Ο 2 Δy Ο 2 Δε Ο π*Δy

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Q: Find each indicated quantity if it exists. Let f(x) = = |x-181 X-18 . Complete parts (A) through…

A: On solving this we will get

Q: Use partial fractions to find the indefinite integral. (Use C for the constant of integration.…

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Q: A B O A OB O OD 1 13 (sin(3z))¹⁰ + C 1 33 ſ cos(3z)sin¹⁰(3z) dz 1 3 (cos (3z))¹¹ + C F None of the…

A: Here we have to find the integral.

Q: For each polynomial function below, indicate the degree, the leading coefficient, and the end…

A: Given :1. fx=-3x4+2x3-8x2+112. fx=8x3+x2+7

Q: Starting from the same point, Angela starts walking eastward at 6 m/min while Jessica starts running…

A: Please see the below picture for detailed solution.

Q: y-values 86 9* 7- 6 5 4- 3- 2 1 g(x) 1 2 3 x-values If f(x) = g(h(x)), then ƒ' (1) = Submit Question…

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Q: Two cars start moving from the same point. One travels south at 60mi/h and the other travels west at…

A: We have to find distance between two car

Q: Evaluate the following integrals. 1. ft³ cost dt 2. f x² e-x dx

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Q: 2 +81 1/s(3² +9) ²0 ds

A: The given integral is (s4+81)/[s(s2+9)].

Q: The range of the function f(x, y) = This option 10, 1/3] [1/3, +00[ O This option None of these 1…

A: Domain:- The set of all those points (x,y)  such that the function at those points exists.Range:-…

Q: Evaluate: lim 8118 x6x² + x²-1 8x6 + 4x³ + 10

A: see below the calculation and answer

Q: Find the following using the table below. I 1 2 3 f(x) 1 3 4 f'(x) 4 1 g(x) 4 1 3 g'(x) 2 3 33 4…

A: Given that h(x) =fg(x). We have to find h'(3) that is derivative at x=3. Now, ddxh(x) =ddxfg(x)…

Q: d dx 0.8 - - 3.4x^2 +6x)

A:

Q: The radius of a sphere is decreasing at a rate of 1/4 cm/s. At what rate is the volume decreasing if…

A: Volume of the sphere , V=43πr3

Q: ) Consider a horizontal parabola of the form ay² +by+ c = x wherea #0 and whose graph contains the…

A: Given problem:- Consider a horizontal parabola of the form ay² +by+ c = x whose graph contains the…

Q: The domain of the function f(x, y) = 3xy 2+√4x2+y2-16 is:

A: Given problem:- fx,y=3xy2+4x2+y2-16  To find:- Domain of f(x,y)

Q: In Exercises 19-24, match the parametric equations with the paramet- ric curves labeled A through F.…

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Q: Wendy took a trip from one city to another, a distance of 480 mi. She traveled part of the way by…

A: We have to find how long did Wendy spend on the train.