II Simplify the following: 1. (ĀNBNČ) U (Ā nBN C)U (ĀNBNČ)U (ĀNB N C) U (A OBNČ)U (ANBN C) a. ĀU B b. В UC c. A UC d. Ā U Č

Q: Questióh 2 of 9 View Policies Show Attempt History Use the formula for the binomial series: (1 + x)"...

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Q: 6 for the Use sigma notation to write the Taylor series about x = function. 1 x+5 k =

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Q: 4. Given: a, = 5, a4 = 13 Find: d =? а. 1 b. 2 с. 3 d. 4

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Q: 9. Evaluate f(e* + 2*) dx a.) 2e* + +C In2 b.) er + 2ln* + C c.) e* ++c d) e* + 2ln x + C In2 10. Ev...

A: Evaluate integrate. And follow step 2nd .  According to guidelines we solve only first three parts. 

Q: 18. If x² + 2xy = y² then y' is b. 2x + 2y d. -x

A: (18). Given: x2+2xy=y2   We know that; The sum/difference rule: f±g'=f'±g' The Power law: ddxxn=nxn-...

Q: xy'= y + 2x'

A: xy' = y + 2x3xy'-y = 2x3Dividing by x;y' -1xy = 2x2 ...(1)Comparing with Bernouli's equation;y'+P(x)...

Q: cot 2x J Tcot22x – 15

A: Given problem:-

Q: Eliminate the parameter to find a Cartesian equation of the curve, for - くtく æ(t) = 4 tan? t y(t) = ...

A: Given

Q: The standard form of the first order linear differential equation x'y'+ry +2=0is

A: The standard form of a first-order linear differential equation is:

Q: Consider dx and using u-substitution in rewriting the integrand as a function of u and du. x(1+Vx) D...

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Q: Determine whether the series converges, and if so find exactly its sum. Otherwise type none in the b...

A: The given series is: ∑k=0∞56k+3=563+564+565+566+... which is a geometric series with the first term ...

Q: Q6) Evaluate the following integral by using Odd and Even Powers Method: | cos* (;x) dx y =

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Q: Obtain the differential equation of the family of circles having their centers on the x-axis.  (x-h...

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Q: Solve the differential equation. 5y' = 4 ex/5 + y + y The solution is y = 4x +C X 5 5 e (Type an exp...

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Q: Solve using the U-Technique Question 8 Given: S . There is a function f (x) such that when u = -x³, ...

A: Given: ∫2f(x)dxe-x3   , u=-x3

Q: sec y x tan y dy 1+ tan y

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Q: 5 Suppose that cos(0) = and 0 < 0<. 13 a. Determine the exact value of sin(0). Enter your answer as ...

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Q: xdy+(y- xy + 2)dx =0 dx=0

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Q: xdy +(y– xy+2)dx = 0

A: The given differential equation is; xdx+(y-xy+2)dy=0

Q: (2x² +)x (x8 + 4x5 + 4x²)2 Using u-substitution and transformation of the integrand, then the power ...

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Q: Find two positive numbers whose product is 324 and whose sum is a minimum. List them in non- decreas...

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Q: Suppose an object in circular orbit stops in a position where cos(0) The terminal point is 13 locate...

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Q: Use the difference a,n+1 – a, to show that the given sequence {a,}is strictly increasing or strictly...

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Q: IV. Find the particular solution of each of the following. 1. (2х — Зу + 2)dx - (3x + 4у-5); у(-3) %...

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Q: Express the repeating decimal as a fraction. 0.451141 41 41.

A: Given data

Q: Find the general term of the sequence, starting with n = 1. Determine whether the sequence converges...

A: Given:

Q: Find the Maclaurin polynomials of orders n = 0, 1, 2, 3, and 4 and then find the nth Maclaurin polyn...

A: Topic:- application of derivatives

Q: Find the indefinite integral. (Use C for the constant of integration.) sin x dx 3 + cos² x

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Q: Is the function given oy 5x-4x-5, メ<5 x-5 2. Fx)=/ メ+1,×25 Cantinucus atX =52 why cir why not Z

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Q: Find the derivative of y with respect to x for y = sinh 1(11/15x). dy 165 dx 2/1815x? + 15x

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

Q: 5x4 dx x5-3 S4 cos (-3x + 2) dx [ 4cot 5x csc25x dx

A: You can solve these integral problems by using the method of substitution.

Q: Solve using the U-Technique Question 15 Given: S 5x? cos 3x³dx. If u = 3x³, then the resulting integ...

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Q: Solve the given differential equation by using an appropriate substitution. The DE is homogeneous. (...

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Q: y = cje* + cze²r y" -y – 2y = 0 O 2y " -y' – y = 0

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Q: If S(16x4 – 16x³ + 4x²)dx = F(x) + C, then F(x) ?

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Q: Find the indefinite integral. (Use C for the constant of integration.) cos5 t dt V sin t

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Q: Consider the integral 2nx g(x) dx. There is a function g(x) such that when u = In x the resulting in...

A: Given query is to find the value of indicated function.

Q: Evaluate the limit. If dne, explain. (2cos(4x² + 7) + [6x² + 4] lim X→+∞ 4x2 + 7

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Q: A Complete the table. du formula answer 24x+2 1. (2x-1)(3x+2) 2. -dx de 3. 4-S 4-3inin2r 4. xp- sin ...

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Q: A rectangular box with an open top has a square bottom and a volume of 4 m³. Find the dimensions of ...

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Q: Solve the following initial value problem for y as a function of x. dy x = /x? - 16, 3x dx x24, y(4)...

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Q: k If u = f(x), then f dx x4+2x²+1 +C for some constant k . Compute kf(1). x2+1

A: topic - functions and indefinite integral

Q: The integral / 2/ (*) cos(2*) dx takes the form k cosu du when u=2* and f (x) =x – 5. what is the va...

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Q: 3T en: S 5x² cos 3x³dx. If u = 3x³, then the resulting integral is S f(u)du. Find f (").

A: Given query is to find the indicated function.

Q: Use sigma notation to write the Taylor series about x = xo for the function. 4 In x; xo = 1

A: Taylor series of function fx at a is defined as:       fx=fa+f'a1!x-a+f''a2!x-a2+f'''a3!x-a3+…=0+ddx...

Q: Write the factored form of the

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Q: Determine whether the series converges, and if so find its sum. If the series diverges, indicate tha...

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Q: Solve the given differential equation by separation of variables. (e + 1)?e-Y dx + (e* + 1)Se-* dy =...

A: Given:- (ey +1)2 e-y dx +(ex +1)5 e-x dy=0 To find :- General equation of given differential equatio...

Q: A Complete the table. du formula answer 24x +2 (2x -1) (Ax + 2)3 d 2. 7Vx - Sx de Se 3nin2 de sin S ...

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Q: Find the derivative of the function at Po in the direction of u. x- 5y g(x,y) = Ро(1, - 1), и%3 3і +...

A: To find the derivative of the function  g(x,y)=x-5y5xy+7 at P0(1,-1)in the direction of u=3i+4j=&lt;...