If f(x) = 10(sin(x))", find ƒ'(2).

Q: Simplify the expression In c. * a. d. 3x Iní3x)

A: topic :- simplification

Q: 1. Find for each of the following: dx d) y = e +x* +e° g) y =x2r-5 h) y = log3

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Q: Find the equation of the parabola with the given properties Vertex (0,0), focus (5, 0). = x

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Q: Find the center of mass of the region bounded by y=2sin(2x),y=0y=2sin⁡(2x),y=0 on the interval…

A: Given

Q: Use the theorem of Leibniz in the following problems: 1. Obtain the n'th derivative of: x2y [x?y") +…

A: The objective of the question is determine the nth derivative of the given equation.

Q: Find all values of x for which the series converges. (Enter your answer using interval notation.)…

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Q: dy Find Y dx (x- 2) - (2x+1)4 if y= | Use logarithmic differentiation. x=0 e2x. Vx+8

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Q: Q3: Find f(t) ( Inverse Laplace Transform )of the following functions s+1 1. F(s) = 2.F(s) (s…

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Q: 3. If Ax) = , find f"(-1). c. 0 d. -1 a. e b. 2e

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Q: In solving Optimization Problems, it is important to substitute zero to the 니o parameter being…

A: Here is the solution

Q: Evaluate the following indefinite integral: 2(1 + e*) dx (x + e*)3

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Q: Use the power series E(-19^x", \xl < 1 n-0 to find a power series for the function, centered at 0.…

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Q: Let y = tan find the differential dy of the function.

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Q: For the function f(x,y,z) = 1 + 2xy¹ − 325, find fx, fy, and f₂.

A: Given query is to find indicated partial derivative.

Q: Suppose that you have the utility function: u (x) = Vx u" (x) 43 %3D Find : u' (x) 1 2x 2x Option 2…

A: I have stated the used formulas in the solution

Q: (D4 – 2D3 + 5D² – 8D + 4)y = 0 (D3 – D² + D – 1)y = 0 (4D3 + 12D2 + 13D + 10)y = 0 (D5 + D4 – 7D3 –…

A: Given

Q: Use the theorem of Leibniz in the following problems: If y=x³e2x find y(m) and hence y(3). julm) =…

A: Leibniz rule states that (f(x)⋅g(x))n=∑r=0n Cr nf(n−r)(x)⋅gr(x) Let fx=e2x and gx=x3

Q: 09. lim, " -т(csc Tх) (Inx)| x)(Inx)]

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

Q: 4. If y = x cos x determine the 5th derivative. [y(5) = (60x – x³) sin x+ (15x² – 60) cos .x]

A: To find out the fifth derivative.

Q: Use the alternative form of the derivative to find the derivative at x = c (if it exists). (If the…

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Q: A spherical snowball is melting in such a way that its diameter is decreasing at rate of 0.4 cm/min.…

A: We know volume of a sphere of radius r is, V= (4/3)πr³ Doing implicit differentiation on both sides…

Q: 2-[x³.e* dx 3- S x².cosx dx

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Q: Exercise 195 Further problems on Leibniz's theorem 8. If y = (x³ + 2x²)e2* determine an expansion…

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Q: 1) Find the radius of convergence and interval of convergence of the series. Show All Your Work.…

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Q: Find the value of dz and dz/ dy at the point A when x changes by (0.01) and y changes by (- 0.01 )…

A: Differentiation need to be done appropriately.

Q: Find d (7ª). Type In(x) for the natural logartihtm function. dx

A: Given query is to find derivative if the expression.

Q: the sum of the series by using the first six terms. (See Example 4. Round your answer to four…

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Q: Find two positive numbers that satisfy the given requirements. The sum of the first number squared…

A: Given :The sum of first number squared and second number is 51

Q: Find the arc length of the curve on the given interval. (Round your answer to three decimal places.)…

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Q: Find the total mass of two turns of a spring with density p in the shape of the circular helix…

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Q: 4. It is estimated that x months from now, the population of a certain town will be changing at a…

A: First we will integrate p'(x) to find the function p(x) and then we will find the population 27 from…

Q: Find all the second order partial derivatives of g(x,y) = x°y + 5 sin (y) + 4y cos (x). 20x°y - 4y…

A: Given query is to find indicated partial derivative.

Q: dy for each of the following: dx 1. Find d) y = eF +x*. g) y = x2-5 1 h) y = log3

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Q: The function f(x) = −2x³+3x²+36x has two critical points, c₁ and c₂. Find them and use the second…

A: We need to find and classify critical points.

Q: Find f, fy. f- f(x.y.z) = 3x - 4y 2. 2 +z?

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Q: Use Green's Theorem to evaluate the line integral (y - x) dx + (2x - y) dy for the given path. C:…

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Q: Suppose f(x, y) : where x = r cos 0 and y = r sin 0. 4 af af and ar Find when r 1, 0 -

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Q: TQ two values of x such that 2x 1. 12x x+41 .a x-1/3 ,x=1 .b x=2, x=-2 .c x-3, x=-3 .d X=-1, x=1

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Q: Find the area of the surface generated by revolving the curve about the given axis. x = 2 cos(0), y…

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Q: 25-x dy dx c)

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Q: Q2:Find the Laplace of the 1- cos(2t) 1. f(t) = t

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Q: After its fastest rate of growth ever during the 1980s and 1990s, the rate of growth of world…

A: We should recognise the t and do the appropriate calculations.

Q: Given csc 0 = -3, sketch the angle in standard position and find cos 0 and tan 9, where e terminates…

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Q: Adah has just bought a new motorcycle for $15 000. The value of the motorcycle depreciates over…

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Q: Which of the following is correct? " 17 3 (3 sinh-(x)) = (coth"(x) = (지 < 1) V - 1 dx Option 1…

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Q: Suppose f(x, y) = xy² + 4. Compute the following values:

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Q: For an arithmetic sequence a31=67 . if the common difference is (-4), find a1 and the sum of the…

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Q: af For the function f(t, x) = sin (9лt + 4x), find at af at (Type an exact answer in terms of t.)…

A: topic - partial differentiation

Q: Find the area bounded 1. 2x2 + 4x + y = 0,y = 2x

A: Sketch the region

Q: For the function f(x.y.z) = 1+ xy° - 4z*, find f f, and f.

A: We can find the partial derivative in the following steps.