Find the derivative, dy/dx: In-2x O y = -() In' 1-4 la > 是 In' x 2/1+2In ४ In' z In z 2w In² z ) In' z

Q: Use power series operations to find the Taylor series at x= 0 for the following function. 17x e* The…

A: we want to find taylor series of the function 17 x ex  about  x=0

Q: Question 5 Determine the derivative of the given function: y = (e + e)3 O y = 3(e- + e")² (e- + e")…

A: The derivative is given below.

Q: 9. 5+ 8 7- 6- 3 5 4 2 g(x) 2 h(x) 1 1 1 2 3 x-values 4 5 1 2 3 x-values 4 If f(x) = g(h(x)), then…

A: Explanation of the answer is as follows

Q: dr 5. 2 ?+3 2

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Q: Find V· (V × F), if F(x, y, z) = 3ei+ 4.xe®j – 2ev²k. V·(V × F) =

A: We need to find dot product.

Q: Graphs of Logarithmic Functions Formulas for the Graphs 5- a. f(x) = – log,(z) 4- b. f(æ) = log,(x)…

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Q: Sketch the region whose area is given by the definite integral. 8. x dx

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Q: / (3Vi-1)dt is 3 -1 by the 2nd fundamental theorem of Calculus. The derivative with respect to x of…

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Q: Find the particular antiderivative of the following derivative that satisfies the given condition.…

A: Solution: C′(x)=3x2 −5x​; C(0)=2,000

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Q: Find the indefinite integral. (Use C for the constant of integration.) 6 + 9x dx (x8 + 1)e*³.

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Q: Find the interval of convergence of the power series. (Be sure to include a check for convergence at…

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Q: dr Vr +3 5.

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Q: Find the eigenvalues of the triangular or diagonal matrix. (Enter your answers as a comma-separated…

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Q: dx 2. o (x-1) 5

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Q: Use Lagrange multipliers to find the extreme values of the function f(x, y, z) = x² +y² + z2 subject…

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Q: A company manufactures mountain bikes. The research department produced the marginal cost function…

A: The increase cost is given by: ∫450720C'(x) dx=∫450720300-x3 dx

Q: In |V Vr+i-2 dt, if we let / Vr+1 - 2, then dt is equal to A 4x°dx None 2(x²+ 2)dx (4x³ + 2)dx E…

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Q: domain: vertical asymptotes l:  x= horizontal asymptotes: y=

A: Given query is to find vertical asymptots and horizontal asymptote.

Q: Use Newton's method to approximate the indicated root of the equation correct to six decimal place…

A: Here, let the given function be: f(x)=x2+ex-9⇒f'(x)=2x+ex Next,…

Q: coso de by trigonometric substitution.

A: answer is in next step

Q: For the matrix A, find (if possible) a nonsingular matrix P such that P-1AP is diagonal. (If not…

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Q: Question 10 sinh a For y= V find y' at x = In2 e* Oy = 0 Oy = 12 Oy = 2/6 Oy =

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Q: Is the mathematical statement correct. If f(x)=f(-x), then f’(x)=f’(-x). Explain why

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Q: 2- find fxx and fyy for f(x, y) = x²sin?y

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Q: Find div F and curl F if F(x, y, z) = xz°i+ 5ytx²j+4z² div F= curl F=

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Q: Let f(x) : Int dt. Find f'(x).

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Q: xp Evaluate the definite integral.

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Q: ||r(t) × r"(t)|| ||r"(t)||* Use the formula k(t) to find k(t). 13 r(t) = 3 cos(3t)i+3 sin(3t)j + tk…

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Q: Q2/ Check the symmetry of r² = -sin(20) %3D Ans./ Symmetry about the origin

A: Symmetry

Q: Solve the separable differential equation dy 0.7y, and find the particular solution satisfying the…

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Q: Evaluate the integral dx (5x + 9)* by making the appropriate substitution: u = dx (5x + 9)*

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Q: Find the Maclaurin series for f(r) using the definition of a Maclaurin series. [Assume that has a…

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Q: Find the area of the surface generated by revolving the curve about each given anis. *- 7t. y= st,…

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Q: A net is dipped in a river. Determine the flow rate of water across the net if the velocity vector…

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Q: Solve the higher order initial-value problem f''(x) = x-1/x + 3 ; f'(1) = 3, f(1) = 0

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Q: (-x+82.762) 1(x) = 0.5e - 25.7 12 М m(x) — 0.15(х - 90)2 — 25.7

A: To find thee first and second derivative of the functions given.

Q: Find the distance from the point to the plane. (5,7,6), 10y +z= 0 The distance is

A: We can find the distance as below.

Q: If f(x) = V19+r² dt , find f'(3).

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Q: Find the area of the surface generated by revolving the curve about each given axis. *- 7t, y= st,…

A: Surface area genarated by revolving the curve about x-axis is parametric notion is…

Q: Consider the indefinite integral dx: (2² + 2)? This can be transformed into a basic integral by…

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Q: Find the particular solution determined by the given condition. F(x) = 3x2 - 2x; f(O) = 9 %3D %3D O…

A: Given query is to find the solution of the differential equation.

Q: 10 8. 10 If f (x) dr= 17 and/ f(x) dx= 12, then f(x) dr=5 A) True Ealce

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Q: Find V x (V × F) if F(x, y, z) = 9xyj+ 6xyz k. V x (V × F)

A: WS have to solve the vector

Q: Question 3 Determine the derivative of In(csc x) cot x Csc I - cot x CS z Previous

A: A detailed solution is given below

Q: Answer the following questions for the function f(x) = a/a? defined on the interval -4 < x < 5. x+16…

A: We need to find concavity and inflection points.

Q: dx (x– 1)%

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Q: Solve y" – 2y = x²

A: We have to find the solution of the given differential equation.

Q: Problem 3 Use the rules of differentiation to to find the derivatives of the function: (a) f(r)= 3rª…

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Q: Solve the initial value problem. 4 y(x) = 4 sec(3.x) tan(3.x) ; y(7) = %3D 3

A: y'(x) =4 sec(3x) tan(3x)y(x)=∫ 4 sec(3x) tan(3x) dx3x=t,dx=dt3y(x)=43∫ sec(t) tan(t) dt     =43 sect…