Given that y = (1In(x))?m(=), find dy using the method of logarithmic dx differentiation. dy dx ||

Q: Let -1 < a < 0 0 < x < 1 1, f(x) = Expand f in a Fourier series. Sketch at least two periods of the ...

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Q: QUESTION 10 How fast is the area of a circle changing when the radius is 10 cm. if the radius is cha...

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Q: Find the transition points. y = 10x - 90x4 (Use symbolic notation and fractions where needed. Give y...

A: Given equation is y=10x6−90x4

Q: Comparison Test: Suppose that > an and) bn are series with positive terms. If n=1 n=1 an = C lim n-o...

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Q: (a) 2(x- 3) + 11 = 6- x x-4 (b) 3+x 三 3 (c) x2 - 7x + 6 = 0

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Q: Find the function y = y(x) (for æ > 0) which satisfies the separable differential equation %3D dy da...

A: Given : dydx=3+17xxy2   , y(1)=6

Q: Find the nth Maclaurin polynomial for the function. 5x - 4 f(x): n = 4 x +1 P4(x) =

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Q: QUESTION 1 9dz 9dz The infinity in the can be eliminated by lim J2 (1- 32)4 t+ o'2 (1-3z)4 True Fals...

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Q: A In27 +C In3 2ln3 (c) +C (D (3+4) 2 +C In9 E None

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Q: Find the general solution of the following Differenti 1. y(y2 + 1)dx + x(y² – 1)dy = 0

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Q: Determine whether the equation is exact. If it is exact, find the solution. (e*siny + 4y)dx – (4x – ...

A: An equation of the form Mdx+Ndy=0 is exact if ∂M∂y=∂N∂xand the solution is given by ∫Mdx+∫Ndy=C  On ...

Q: 10. Find the equation of tangent line to the graph of f(x) = 2x – x³, at the point(-1, –1). %3D

A: Find your answer below 

Q: 1. Determine the following information regarding each function step by step and then sketch its grap...

A: Let's find. 

Q: Evaluate: lim sin(3x)cot(2x) O a. 2 O b. 3 2 O c. 3 O d. 2 3

A: limx→0 sin3xcot(2x) limx→0sin(3x)cos(2x)/sin2x so now it form 0/0 so we use la'hospital rule differe...

Q: sin 3t? limt-o 1-cos 2t

A: To evaluate: limt→0sin 3t21-cos 2t 00 form

Q: Determine whether the differential equation (2x2 - 2xy + 4) dx + (4y- + 2) dy = 0 is exact. If it is...

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Q: 2 Determine the value of the series n(n + 2) 1.833 0.833 -2.167 2.833 The series is divergent.

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Q: Given the graph below, evaluate the following limits: y = b Retrieved from:basiccalc_initial_release...

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Q: Let V(t) = t – 6t + 8 represent the velocity after t seconds of an object in meters per second. (a) ...

A: we haveV(t) =t2-6t+8

Q: sec x (Ъ) у -

A: Let's find. 

Q: Use the binomial series to find the Maclaurin series for the function. 1 f(x) = (1 + x)4 f(x) = > n ...

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Q: 5. Let f(x, y) = 3xr² + xy- y. (a) Compute f(1.02, 1.99) exactly. (b) Let f(1.02, 1.99) = f(1+0.02, ...

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Q: (x* + y° ) In (x² + y* ). (x,y)= (0,0) f(x, y) = k +1, (x, y) = (0,0)

A: If f is continuous then lim (x, y) tends to (0, 0) =k+1 And using l hospital rule. 

Q: Without the aid of Wrongskian, determine whether the given set of functions is linearly independent ...

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Q: substitution

A: We have to find value of the given definite integral according to the given information

Q: An integral expression for the area of the surface generated by rotating the curve X=VV.1sys8about t...

A: here limit of x is from 1 to 2   A=2π∫12f(x)1+f'(x)2dx so here f(x) = y = x3 f'(x) = 3x2 (f'(x))2 = ...

Q: Let x, Y be positive real numbers. If x2 – y² =1, then x or y (or both) is not an integer.

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Q: (a) S(-) dx 2+1 (b) [ 3xV3 dx

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Q: Example 19: (a) Ifx +y = 25, find dy/dx.

A: We have to calculate dy/dx

Q: A curve has an equation of y = x° - 6x + 9x + 2. Find the maximum point of the curve. O (1, 6) O (3,...

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Q: Find the interval of convergence of Σ (х - 6) In (5n) n=2 (Use symbolic notation and fractions where...

A: Interval of convergence is given below.

Q: dy et y = (x³ – 18x)m(=). Find using the method of logarithmic dx - ifferentiation. Express your ans...

A: Topic:- derivatives

Q: Find the interval of convergence for the given power series. Use interval notation, with exact value...

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Q: х If f(x) = cos(1? + 1) dt, then find f'(x). %3D Select one: O A. None of the others O B. sin(x + 1)...

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Q: EX+ Prove that [X Ju cx)] = x'Jr-, cx) Solp 2. ヘャut 2m+2V (-1)" X 2m+V (m!)P(m+v+1). neno 2m+2U-1 (-...

A: Property of gamma function: Γ(m+1) = mΓ(m) ............. (1)

Q: Find fy if f(x, y) = sin 5x cos 5y O fy = 5sin 5x sin 5y fx = cos 5x cos 5y O fx = 5cos 5y cos 5x fx...

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Q: A curve has an equation of y = x - 6x2 + 9x + 2. Find the point of inflection of the curve. O a. (1,...

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Q: Find Zx if z = In. In y 1 – In y Z x Zx = 1/x In y

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Q: Set up the itegral that represents the length of the curve for 4=L x4 +L 4x2 for 12x< 2. Do Not eval...

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Q: - Use integration by parts to show that if f has an inverse with continuous first derivative, then (...

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Q: Find y" if y = x + (x + 2)³ when x = 1 О а. 28 O b. 16 О с. 9 O d. 18

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Q: If 10 5 f(x)dx = 10 and f(x)dx = 5 %3D then 10 f(x)dx is equal to Select one: O 5 O -5 -10 none of t...

A: here given that ∫110f(x)dx = 10  ∫15 f(x)dx = 5 so we have to find  ∫510 f(x)dx = ?  ∫510f(x)dx =∫11...

Q: Find T(t), Ñ(t), B(t), and curvature k for the following curve. (The curvature is constant.) 7(t) = ...

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Q: QUESTION 4 Find the equation of the tangent line to the curve at (1, 4). y = x' + O a. x = 1 O b.y =...

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Q: ass weighing 20 pounds stretches a spring 6 inches. The mass is initially released from rest from a ...

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Q: 8. Find when x = t3 -t and y = 4 –- t². dx'

A: Here, the given functions are: x=t3-t &amp; y=4-t2⇒x'(t)=ddt(t3-t)=ddt(t3)-ddt(t)=3t2-1    y'(t)=ddt...

Q: Find power series representation for f(x)=1/(10+x)^2 and f(x)=1/(10+x)^3.

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Q: 1 dx x2 + 3 3. dx x6 + 3 4. cos² (x) dx x² + 3 5. A. The integral is convergent B. The integral is d...

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Q: Evaluate: A 3 2(,s–3) (c +C 15 4lnr None

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