2. (5 points each) INSTRUCTIONS: Differentiate the following func- tions (respect to a) using any method. (a) f(x) = √x + 2x x (b) f(x) = x sin-¹(x)

Q: Solve the following initial-value problem: y'=x³ - 2xy; y(1) = 1 Ⓒ2y=x²-1+2e¹-x² 2y²=2x²-1+e¹-2…

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Q: erentials and first approximations nd first approximations to the expressions below, and compare…

A: Solution of the problem as follows

Q: Carefully verify that the piecewise function f(x) = x ≤ c {(8-0)² 72 0 satisfies the differential…

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Q: Is x+1 a factor of 5x^4+2x^3−2x^2+3x+1​?

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Q: Question 2 i differential equation 1: Consider the following 2 = y + ==Y y = t4e-4t y 3 a) Is the…

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

Q: Find the volume of the solid generated by revolving the given region with its boundaries about the…

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Q: A water tank in the shape of an inverted circular cone has a base radius of 2 m and height of 6 m.…

A: Let h meter be the height of the water at any time t. Let the angle of the cone be 2α Therefore, Tan…

Q: Let f(u)=u^3 and g(x)=u=6x^4+2. Find (f o g)'(1).

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Q: A function f has the form  f(x) = a + b ln(x). Find f if it is known that  f(1) = 4 and  f(2) = 13.…

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Q: Find an equation of the tangent line to the curve y = 8 arccos (즐) at the point (1,7).

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Q: Solve the following DE: (1+ y² + xy²) dx + (x²y + y + 2xy) dy=0 O2y²+x²(1+x)²=C O 2y²+x²(y + x)² =c…

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Q: 1. Consider a polynomial function f(x) = co + c₁x + c₂x² + ... + Cd-1d-1 + card. A. Applying the…

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Q: Find the area of the surface generated by revolving the curve y=√√2x-x², 0.5 ≤x≤ 1, about the…

A: Surface area generated by revolving the curve y=f(x) about x-axis over the interval a≤x≤b is…

Q: The following differential equation can be reduced to the linear equation by the 1 substitution u =…

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Q: 11. Determine whether the series Σ» (1) n=1 converges or diverges. If it converges, find its sum.

A: Given series:- ∑n=1∞lnnn+1

Q: Differential equation: Initial conditions: -=4e¹1-e¹j+9e³k dt² r(0) = 7i+4j+3k It=0 -2i+ 3j =-

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Q: The integrating factor for the following differential equation is -7 dy +=y= dt O None of the others…

A: To determine the integrating factor for the following differential equation.dydx+-7xy=e-1x

Q: 6. Find Indefinite integral. Show all your work + √(x² + 5x) dx

A: The given integral is: ∫x4+5x dx

Q: Show algebraically where the tangent line of the function r=1+cos theta is vertical and where the…

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Q: Find d2y/dx2. y=5x3/3   -2x

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Q: Ət A. Use the chain rule to find and as functions of x, y, s and t. Ət = მა Suppose z = = B. Find…

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Q: circle with radius 2 miles. Find the length of an arc with angle 90° in a mi

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Q: Find the curve's unit tangent vector. Also, find the length of the indicated portion of the curve.…

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Q: Consider the differential equation -ly"" + 2y" + 1y' - 4y = 0 with y(0) = 0, y'(0) = 1, y" (0) = -4.…

A: Please see the below picture for detailed solution.

Q: 1: Consider the differential Question 1. equation : y cost + 2te" + (sint + t²e³ - 1)y' = 0. a) Show…

A: A differential equation of the form M(t,y)dt+N(t,y)dy=0 id said to be exact iff, ∂M/∂y= ∂N/∂t

Q: Xight only for a 99% confidence interval when n 18.

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Q: Find an Indefinite Integral. Show all your work 3x-4 dx X

A: Topic - Indefinite integral We are given ∫x3x-4dxwe know that∫xndx=xn+1n+1+C

Q: b=? The following equation is exact if (bxy²+4)dy=(7x-4y³) dx O 12 O-12 04 O None of the others -4

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Q: 11. fcsc¹⁰x cot xdx

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Q: ind the inverse Laplace transform "(t) = L−¹ {F(s)} of the function (s) : = S- 8 s² - 8s + 20 -1…

A: Topic:- application of integration

Q: Find the values of x for which the series converges. (If the answer is an interval, enter your…

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Q: Suppose F(5) = – 7, F(9) = 4, and F'(x) = f(x). 5 9 6f(x) dx =

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Q: 5- find a, b and C if w= a.tan (x²+1)_baxy + cryin (z) t-2 and Z=2t²_ze 2 x= zt², J = ze wy =…

A: z = 2t2 - 2et-2  At t = 2, z = 8 - 2 = 6 dz/dt = 4t - 2et-2  At t = 2 dz/dt = 8 - 2 = 6 x = zt2  x =…

Q: A quadratic function f is given. f(x) = x² + 4x + 3 (a) Express fin standard form. f(x) = (b) Find…

A: Let's find standard form , x and y intercepts, vertex, domain and range.

Q: K Evaluate the integral. S ²+2y-3

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Q: For any two nonparallel and non orthogonal vectors a and b with angle between them, it holds that…

A: Note:- Since you have asked multiple question As per our policy, we will solve the first question…

Q: Question Evaluate the sum of the series Provide your answer below: n=0 n+1 53n-1 = n+1 53n-1 Enter…

A: Let's find sum of given series.

Q: Find the limit or indicate that it does not exist. 3 HET [ ( = = 1 ₁ + (000 + ) ₁ + [Tam ² ₁] ] lim…

A: put limit value as  t=π

Q: If f(x) = f'(x) = 9x + 5 7x+5' F what's f'(x)?

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Q: Question 1. equation : y cost + 2te³ + (sin t + t²e³ − 1)y' = 0. 1: Consider the differential a)…

A: I am going to solve the given problem by using some simple calculus to get the required result.

Q: Find an equation of the tangent plane to the surface at the given point. f(x, y) = x² - 2xy + y²,…

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Q: The dosage for a certain type of chemotherapy drug depends on several parameters of the particular…

A: We have to find the formulas for D and c that give D as a function of​ c, and c as a function of w.

Q: (x) x + 1/2 Ax² + Bx + C (x² + D)²

A: Topic:- application of derivatives

Q: For which of the following values of B, the function f(x) is continuous everywhere? f(x) = 3-√√√x…

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Q: Find the implicit equation of the tangent plane to z = e² + x + x² + 11 at the point (7,0, 68).

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Q: → Limit Review! Evaluate the following limits: lim lim ln x = In x = x →0* a) d) x →∞ lim x → 2+…

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Q: x + y - 4 (x,y)-(2,2) √√x+y-2 lim O Ninguna de las anteriores 00 04 O-4

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Q: Evaluate the integral using cylindrical coordinates: fff³ 3 sin(x² + y²) dx dy dz

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Q: what is the answer to question 1

A: We have to tell the linear approximation of f(x)=square root of (1+x)

Q: 60. Total cost from marginal cost. Solid Rock Industries determines that the marginal cost, C'(x),…

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