Find the radius of convergence, R, of the series. 00 (x-4)" n+1 n = 0 R = 1 Find the interval, I, of convergence of the series. (Enter your answer using interval notation.) I =

Q: X912 65. f dx is equal to - √1+x" (A) = log(x² + √√x+1)+c 7/2 (C) 2√1+x" +c HT (B) log +C x" 11/2…

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Q: How. Solve the diff. e que (4y-cosy) dy/dx=3x² = 0, y(0) = 6

A: (4y -cosy)dy/dx -3x2 = 0 y(0) = 0 here we do this using sepration variable method

Q: 14 Given the triangle answer to 4 decimal places. X find the length of side x using the Law of…

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Q: A spherical ball of radius 3 cm was dropped into a conical vessel of depth 8cm and radius of base 6…

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Q: Limits 8. Find the indicated limit using the graph of f(x) below. , V lim f (x) x-2 =

A: Topic = Limits

Q: 41.) If f (x) = )=√(₁ (A) 3-e/4 4 tan(Cnx) +- (B) dx & f(1) = 0, then f (e/4) is - 3-e/4 4 (C)…

A: We need to choose correct option.

Q: 1 Sa dy secy tany S sin ²x cos²x dx 2. S

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Q: Q2: The equation of the tangent line to the graph of y=t² and t = 4x² at t = 1 is (not that x is…

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Q: Determine the area of the shaded region. 14r y=7x-x² 12 10 y=x 2 (6,6) 8

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Q: Q2: The equation of the tangent line to the graph of y=1² and 1=4x² at 1=1 is (not that x is…

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Q: 17 Simplify cot(arcsec 1) undefined 1 0 -

A: Given problem:- Simplify cot(arcsec(1))   undefined 1 0 -1

Q: a body at a temperature of 50°F is placed in an oven whose temperature is kept at 150°F. If after 10…

A: We can use differential equation or Newton law of cooling to solve the problem

Q: Test the series for convergence O a. the series diverges O b. the series converges ∞ 3k k-1!

A: We need to evaluate the convergence of the series :

Q: y''+2y'+2y=r(t), where: r(t)={10sin2t if 0π ; y(0)=1 ; y'(0)=-5

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

A: Solution: L-1 {1/s7}

Q: For the function f(x) = 2x², find the difference quotient ƒ(a + h) − ƒ(a) h 4a + 2h h 4 a² + h 4 a +…

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Q: 2) The expression 321 x 320 x 319 x 318 can be simplified as nPr. The value of n + r =

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Q: Q. Solve the following Initial Value Problem (IVP): y + 3y + 2y = 6e-t at y(0)=1 and y (0)=2

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Q: Problem Let y = f(x) denote the function defined as x² + x - 2, if x 2. -

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Q: Evaluate dy/dx using implicit differentiation.

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Q: 4.² / S² p² sin & dp do dº JTT/2 J1

A: To sketch the region of the integration.

Q: Solution: Here f(t) = 24,0 < + <l 0,1 < t <2 Here period of f is 2L = 2 L = 1 ". The Complex Fourier…

A: Given problem:-

Q: Let R be the region below enclosed by the curves r = 2 - y², y = − sin (7₂2), and x = -1, as shown…

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Q: Q4: Let y=√ and 1= x² then y) = 0 if n= a) 2 b) 3 c) 4 d)5 e) others

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Q: Matrixes: find k by determinant K-3 0 1 A = 1 K-3 0 0 1 K-3

A: We have to find K by determinant.

Q: h(x) = [(x − 3)√6x − x² + 9 sin¯¹ (x-³)] g(t)e-2t (1+e-2t)-1/2

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Q: arccot x arctan x arccos x arcsin x arccsc x arcsec x

A: Given that the inverse of trigonometry function  To find the domain

Q: Q3: The equation of the tangent line to the graph of y=f(x) at x=-3, f(-3)=2 & f'(-3)=5 is a)…

A: Topic:- geometry

Q: Let C be the curve of intersection of the parabolic cylinder x² = 2y, and the surface 3z = xy. Find…

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Q: -. (ex. + Iny + 2) dx + +In+siny) dy = 0 sin y)

A: To solve the given differential equation

Q: L 2 S 5 + 64

A: Laplace Inverse Transform of  function 5s2+64

Q: Convert the polar equation r² = 2 cos (-20) to a Cartesian equation. (x² + y²)² = 2x²-2y² (x² + y²)²…

A: In this question, we want to convert the polar equation in Cartesian equation.

Q: = 3. Let R be the region bounded by y = √x and y 2. Find the volume of the solid generated when R is…

A: Washer Method : Suppose that the f(x) and g(x) are continuous and non-negative function on a,b and…

Q: @ y = x tan 2x

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Q: Q1: If y=sint and t= sin x, then at x = a) 0 b) c) cosl dx² d) -cosl e) others

A: I have stated the used properties in the solution

Q: Find the function that passes through the point (1,2) and whose derivative is dy/dx = (2/x^3) - 4

A: Topic:- application of integration

Q: Use point-slope form to find the equation of a line that contains the points (100, -40) and (20,…

A: Given, (x1,y1)= (100,-40) (x2,y2)= (20,-5)

Q: In how many ways can a family of seven be seated at a round table if two brothers must sit together?…

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

A: We use the formula: For n = 1, 2, 3, . . .

Q: ·S √ 6. dx x² - 4x + 13

A: ∫1u2+1du = lnu+u2+1+C

Q: Solve integration by (udv x cos(x) dx

A: The integration of the integral is xcos(nx) limit 0 to pi/2. Repost the next question.

Q: udv = uv J to Explain why the substitutions below are inappropriate. Let u = e 1. Suppose we apply…

A: Here, to evaluate: ∫xexdx using integration by parts.

Q: Problem 3: ( >>> A bacteria culture starts with 500 bacteria and doubles in size every half hour. •…

A: Topic:- function  Note :- as per our guideline if more than three subparts posted than only first…

Q: MATHS HOME A 41. If f (x) = f[ta (A) 3-e^/4 4 J'a (B). tan((nx) +- dx & f(1) = 0, then f (e/4) is -…

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Q: dx 5. ≈ 16 x J dx – x2

A: This is a problem related to integration. Based on the general formula and concept we will answer…

Q: Find the area of the region between the graphs of y = 16-2² and y = -4≤ ≤ -1. The area is 2x+8 over…

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Q: MATHS HOME A 41. If f (x) = f[ta (A) 3-e^/4 4 J'a (B). tan((nx) +- dx & f(1) = 0, then f (e/4) is -…

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

Q: The volume of the solid whose base is region in the xy-plane that is bounded by the parabola y = 12…

A: Concept: To find the limit of x put equate the values of y  The volume of the solid in the x-y plane…

Q: C. d. = cos(√x + 3) dx [x³√x² +1dx

A: We have to solve given integration.

Q: Chapter Four d'y df² and y'(0) = 3. 2. 9. dy 24 +16y=0, dt given y(0) = 3 y =(3-1) e3

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