Question Given f(x) below, find f'(x). Provide your answer below: f'(x) = f(x) = fot t¹ dt

Q: Find the indefinite integral. S Step 1 / sin sin³ 70 √ cos 70 de To solve the integral Therefore,…

A: Solution

Q: 5. Find (In 3) for a solution (y + x² e) dx - xdy = 0; y(ln 2) = 0 (x) to the initial value problem…

A: The given equation is; (y+x2ex)dx-xdy=0; y(ln 2)=0

Q: The linear approximation at x = 0 to sin (7x) is A + Bx where A is: and where B is:

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Q: Find curl(4z i+ 5x j + 7y k). curl(4z i + 5x j + 7y k) = ( i )i + ( i )j + ( i )k

A: Topic- Curl of a vector

Q: Find the average value of the function over the given interval. (Round your answer to three decimal…

A: Note: As per our company guidelines we are supposed to answer the first question only. Kindly ask…

Q: equa 5 itions all approach y = 4 = 5 5 4 a - Y as t →∞. dt

A: Topic:- application of integration

Q: A dolphin dives down into the ocean and resurfaces along a path that is modeled by x² - 8x + 4y = 0,…

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Q: Solve the initial value problem y" — 2y' — 35y = 0, y(0) = a, y′(0) = −15. Find a so that the…

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Q: handwritten

A: Please refer to the image below

Q: A firm faces a marginal cost (MC) function: MC = 50 - 10Q+Q² (where Q represents units of output).…

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Q: If Nx - My M equation = Q, where is a function of y only, then the diffe has an integrating factor…

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Q: Find the minimum value of the function f(x) = 2x² +18.3x + 45 to the nearest hundredth. Answer:…

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Q: Find the area of the region bounded by the graphs of the equations. Use a graphing utility to verify…

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Q: Consider the following. Let u = 3x³ - 1. Find du. du = dx dx Indicate how the limits of integration…

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Q: Find the value of b for which the differential equation (ye5ay + x) dx + (bxe5y) dy = 0 is exact,…

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Q: Determine whether the following series are convergent of divergent. If it is convergent, find its…

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Q: Sketch both parametric curves below. Then determine if they intersect they intersect, find the point…

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Q: Farmer Jones, and his wife, Dr. Jones, decide to build a fence in their field, to keep the sheep…

A: Topic - Area between curves

Q: f(x, y) = 9xye(x² + y²) f(0, 0) = f(0, 1) = = f(1, 1) = ==== f(-1, -1) =

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Q: Determine all critical points of the function f(x) = 2x(4- x)³.

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Q: f f(c)=0, then f(c) is a relative maximum or a relative mi Always Be My Baby Sometimes Love Just…

A: Topic:- calculus

Q: 5. Matiu is a talented furniture maker and has decided to build a bike frame out of wood. He likes…

A: Given: the two triangle connected to each other as shown in the question.

Q: Find the curvature and the radius of curvature at the point t = 0. x = e cos(t), y = e sin(t), z =…

A: Basic calculation of vector is required

Q: Find the derivative of the function. f(x) = arcsec(4x) 4 f'(x) = 4√ 16x²2 - 1 or 1 x√ 16x² - 1 X

A: As we know that the derivative os sec inverse x is: ddxsec-1x=1xx2-1

Q: Find the limit, using ALGEBRAIC techniques written down (not just by graphing): lim x →9 √x - 3 X -9

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Q: Question 8 Find f'(a) for f(a) O f'(x) O f'(x) O f'(x) = O f'(x) O f'(x) cos - 1 cos? an cos - cos 2…

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

Q: Find f"(x) for the function. f(x)=(7x^2-2)^6

A: Find f"(x) for the function. f(x)=(7x2-2)6  Derivative of y= (ax2 +b)n  y'= n(ax2 +b)n-1.(2ax)  And…

Q: Find a differential equation whose general solution is 7t y = c₁e¹t + c₂e-2t. y" - 5 y' - 14 y = 0 ✓

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Q: r = 17 sin 2t i - 17 cos 2t j

A: Given equation r= 17 sin 2t i- 17 cos 2t  j

Q: The traffic flow rate (cars per hour) across an intersection is modeled r(t) = 300 + 900t - 270t²,…

A: Topic = Algebra

Q: 3 -6 -4 사업 4 2 -2 19 6 ly 2 4 6 8

A: Given,

Q: ² x (√x + √x) dx

A: We know that integration power rule is  Integration of xn is xn+1/n+1 + C. Here C is integration

Q: sin 2xdx 2+cosx

A: Our Aim is to evaluate the given indefinite integral using U-Substitution.∫sin (2x)2+cos (x)dx-(i)

Q: TE: Use c for the constant of integration. 3 t²54 t + 486 + 9y' +y = 3t² C es utions converge to the…

A: Topic:- differential equations

Q: Which is the focus and directrix of the parabola with equation (y + 0.5)² = 4(x - 1)? Focus…

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Q: dN dt The rate of change of N is proportional to N. (Use k for the propor kN N(t) = Cekt Evaluate…

A: We are asked to find the value of N when t = 3

Q: Differentiate from first principle y = 5x²³² +22² +32 +4

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Q: Find V (F x G), if F(x, y, z) = 13xi +j+ 7yk and . G(x, y, z) = xi + yj - zk. V. (Fx G) =

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Q: A deposit of $9,000 is made in an account that earns 5% interest compounded quarterly. The balance…

A: The given data is: The balance in the account after n quarters is: An=90001.0125n

Q: Shared with me > 2011- Files Find the Wronskian of two the functions y₁ = cos41_g(t) = e' cos(t).…

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Q: Use appropriate algebra and Theorem 7.2.1 to find the given inverse Laplace transform. (Write your…

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Q: 3. dy= 2x+y dx x+2y

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Q: Which are the foci for the hyperbola modeled by the equation (Y-32 (x-1)² _ -1? 36 13

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Q: Use the formula k(t) k(t) = "(t) || ||r' (t)||³ r(t) = 11 cos(3t)i + 11 sin(3t)j + 2tk ||r' (t) = to…

A: The given formula is; κt=r't×r''tr't3 And rt=11cos3ti+11sin3tj+2tk   As we know the Chain rule:…

Q: Consider the following. W = xyz, X = S + 2t, y =s - 2t, z = st² (a) Find aw/as and aw/at by using…

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Q: Suppose f(x) = x² 11 (a) The rectangles in the graph A illustrate f(x) on the interval 4 ≤ x ≤ 8.…

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Q: Find div F and curl F if F(x, y, z) = 10y³zºi – 8x³z¹ºj – 5xy³k. div F= curl F=

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Q: Find a vector function, r(t), that represents the curve of intersection of the two surfaces. the…

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Q: units

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Q: Describe the graph of the equation. r = 18 sin 3ti - 18 cos 3t j O It is a circle of radius 18 in…

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