Consider the following function. f"(x) = 48x Find f'(x). (Use C for the constant of the first antiderivative.) f'(x) = Find f. (Use D for the constant of the second antiderivative.) f(x) =

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Q: Direction: Find the antiderivatives of the following functions using substitution rule. 1. S(5x +…

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Q: 4. E+sec"x+1\dx

A: Solving the problem by finding the value of the integral.   NOTE :: As per our Expert guidelines we…

Q: the Q2, Find hergth of o polor Curve ア= B4 Use this formula dr de

A: Given:  The polar curve is given byr=eθ2 To Find:  To find the length of the given polar curve by…

Q: x+y Q3) Evaluate triple integral S dz dx dy. x-y

A: To evaluate the triple integral ∫02∫0y∫x-yx+ydz dx dy.

Q: EVALUATE THE LAPLACE TRANSFORM OF THE GIVEN FUNCTION USING APPROPRIATE THEOREMS. f(t) = t? cos 2t.…

A: Answer is in below steps.

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Q: (-1)" V2n2 + 5 Given: power series > (x + 1)" n=1 ii. Find the interval of convergence of the power…

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Q: GIVEN THE FOLLOWING POWER SERIES REPRESENTATION BELOW: x4 + 4! Cosx = 1 - + 6! .. 2! (-1)"x2n (2n)!…

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Q: Q3) Evaluate triple integral , dz dx dy.

A: We can calculate this as follows:

Q: Given that h(x) sin(2x + 1), determine functions f(x) and g(x) such that h(x) = f(g(x))

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Q: +o0 In(tan -1 x) dx 1+x2 1

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Q: Using exact differential equation, determine the solution of: dy y-- 2x = 3y2 – 2 when y = 1 and x =…

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Q: Evaluate the integral. (Use C for the constant of integration.) cos a da sin a

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Q: Calculate the derivative of the function xe" at the point x = 0 %3D O 1 e O 2e

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Q: FALSE if otherwise. Prove your answer. (b) If the power series > an(x + 1)" converges at x = 2, then…

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Q: Q3) Evaluate triple integral , dz dx dy.

A: Topic = Integration

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A: As per rule of bartleby we can solve only one question at a time and we can solve only three subpart…

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Q: (Basic Differentiation Rules Basic Calculus) Kindly answer 1-3 and show complete solution. thank…

A: Formula:ddx(a f(x))=a  ddxf(x)ddx(xn)=n xn-11)f(x)=10 x10f'(x)=10 ddx x10f'(x)=10 10 x10-1f'(x)=100…

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Q: 5. In antidifferentiation, the formula f x" dx = (n+1) + Cis valid if? A. nER 6. In item number 5,…

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Q: Find an equation of the line that is tangent to the graph of f and parallel to the given line.…

A: Given problem:- f(x) =x2 ,  Find equation of tangent line which parallel to line 8x-y+16=0

Q: TOPIC: Partial Fraction Decomposition 1. J: 2х3 —х2+2х-2 dx (х2-2х+2)x2

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Q: Find an equation of the line that is tangent to the graph of f and parallel to the given line.…

A: I am attaching image so that you understand each and every step.

Q: Use tabular method to evaluate ſ –2x³e¬5* dx -5x 1.

A: Let's find.

Q: In evaluating Sx²V1+x dx with u = V1+x, what is dx equal to ? u du a. b. и du c. 2и du 3. d. • 2 и…

A: Since this is a multiple question, according to the Bartleby answering rule, only first question is…

Q: derivative of f(x, y, z) = x + z at P(6,5,-5) in the direction from P to Q(5,7, -4). NOTE: Enter the…

A: We can solve this as follows:

Q: x² +64 Using trigonometric substitution, given dx, the simplified form of the integral is= sec ede…

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Q: du 2. f 1-cos? 2u

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Q: If 42 | f(x)dr = 10 %3D 59 and 42 | 9(z)dr = 30 59 and 42 |. h(x)dx = 32 59 what does the following…

A: Use additive property of integral

Q: 2. Use integration by parts to evaluate the following. (a) S x tan-x dx

A: Given

Q: B.) Function; x- 2x - 15 3.) f(X); f(5) = 4.) f(t) = f(3000) = 3000 X- 5

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Q: f(x,y) = 5 + Vx – y² +4

A: To determine theb domain and range of the following function.fx, y=5+x-y2+4

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Q: Find the solution of the corresponding inhomogeneous system of equations: z+y+ 2z = 8 z+ 2y + 2z 2z…

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Q: eries 1)" 2 + 5 rmine if the resulting series of constant terms wh ely convergent, conditionally…

A: We have to find the following conditions according to the given information

Q: Determine whether the series is convergent or divergent. En=1 (-1)"3" 2 -1 4"

A: Root Test: Suppose that we have the series ∑an. Define,  L = limn→∞|an|1n Then, If L<1 then the…

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Q: 1-5 by Partial funtron x-16

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Q: 3 Figure 1: Graph of f 4. Each of the following is true EXCEPT: lim f(r) = 0 c. lim f(r) = +o∞ a.…

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Q: Q2) Solve the D.E dy + (xy-xy?)dx = 0

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Q: | 3xV3x2 + 4 dx = -. 2 (3x2 + 4)V3x² + 4 + c 3 1. O -;(3x? + 4)V3x2+4 + c 2. O 1 (3x² + 4)v3x² + 4 +…

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Q: 4) V9-z zt2-6

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

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Q: 2. Use integration by parts to evaluate the following. (b) S 3x³V1– 2x³dx -

A: Let 2x3=t then solve it.