Find the solution of y' = 2(2x-y) which passes through the point (0, -1) the answer should be y=2x-1

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A: We will use integral by parts to evaluate integration of arc sinx

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A: We neee to find derivative of y for the function given below:

Q: 2. Find the 11th term of the following geometric sequence. 4, 12, 36, 108, ...

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Q: For the straight line defined by the points (1,57) and (3, 87), determine the slope (m) and…

A: Solution is done in step 2

Q: Given: y = arctan sinh find y' at x = 2 %3| cosh 1 %3D 1+sinh? 1 cosh 1 O y = %3D 1+sinh 1 cosh 1…

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Q: Find the first partial derivatives with respect to x, y, and z. 7xz x+y

A: This question is related to differentiation, We will solve it using given information.

Q: f(x)= 3sin Vx' – 3x + 2

A: Solution:

Q: 1. Find the area bounded by the parabola y=4ax, the x-axis, and the lines x=4a, x=9a.

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Q: Differentiate the following function y = e log(4") You may use Insert -> Equation to help you input…

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Q: Find div F and curl F if F(x,y, z) = x°i – 11j + yzk. - div F= curl F=

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Q: 3. y = In? (csc2x). Find y"

A: y=ln2(csc2x)

Q: Find y': y = ar cos

A: The given function,  y=ar cosx3

Q: Consider f(x) = (5x + 11)2022, find: i. f'(x) ii. f"(x) iii. f''(x) iv. fiv (x) v. f°(x)

A: Given, f(x)=5x+112022

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Q: 13. Compute the Laplace Transform of f(t) = t°e" +e* sin3t. 4 1 A) (s+ 2)'s² +4s + 13 2 B) (s –…

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Q: Use a change of variables (Substitution Method) to evaluate the following definite integral. Show…

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Q: 2 and common ratio Write down the first four terms of the geometric sequence with first term (Type…

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Q: SHOW THAT THE DIFFERENTIAL EQUATION IS LINEAR EQUATION OF ORDER ONE 3. Vdx + (2x +1 – Vx)dV = 0

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Q: 11 ti + dt

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Q: x³dx Using trigonometric substitution, is equivalent to x²-4 8 / sec*o do A B 6 tan'o seco do © •Smo…

A: The given integral is: I=∫x3dxx2-4

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Q: 1.f In(x² +a°) dx Ans. x In(x' +a')- 2x + 2a tan " +C a

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Q: Question 5 Given the expression below, y = ecos" arcsec(ln(r 1)) determine y. Upload Choose a File

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Q: In the year 2000, the population of a small city was 43,000. The population grows at a rate of r(t)…

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Q: For the given function find dy/dx. = x + 2 %3D O y = 1-y-3x2-4x %3D 3y2 +2+2 O y = 1-a+3y-4x 322-y+2…

A: We know Implicit differentiation of ax+by=c is given by, a+bdydx=0 ddx(xn)=nxn-1 , for any real…

Q: Find r'(t) r(t) = 6Vti + t²V¢j + In(2 )k r'(t) =

A: Given r(t)=6ti+t2tj+ln(t2)kThat is…

Q: 3. Evaluate (D +x)(D–x). Note: D=- (denotes derivative with respect to x). A) D²-x² B) D² -x² - 1 C)…

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Q: For the given function find dy/dx. = x +2

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Q: 21 Given 3x7 +8x5 - , determine, y" O 630x4 + 480x² + 126 5x4 O 840x3 + 360x 504 - 504 O 2520x3 +…

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Q: test conerg ence and clivergence h!

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Q: Find the divergence of the vector field F. F(x, y) = 7XEX¡ – 9x²y2j

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Q: 1+2x2 dx J x2(1+x?)

A: A detailed solution is given below

Q: Calculate the arc length of the curve f(x)=(2/3)(x²+1)ª2) in the interval [–1,1]

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Q: Find the following for the given equation. r(t) = 8 cos(t)i + 8 sin(t)j (a) r'(t) = (b) r"(t) = (c)…

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Q: æ = (f+ a)soɔ Which among the choices is equal to the dy/dx? In your sc - cos(r+y) A)

A: Given: cos(x+y)=x

Q: Ex: Investigate the convergence of the following series. H.W 1 7 2) ΣΥ-1 3n 2n+5n IL !

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Q: Find if possible the limit of the following sequence: x[k] = ,k = 1, 2, 3, . The limit is (Type an…

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Q: Given f(x, y) = (3x – a²)(2y – y²). (a) Find all the critical points of the function. (b) Classify…

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Q: 2. Find the Area bounded by the curve y=4-x2 and the x-axis.

A: 2. The area bounded by the curve y=4-x2 and the x-axis Note:    Multiple questions are given, we are…

Q: Question 2 Find the inverse Laplace transform of H(s) - (;+)-

A: H(s)=1s2-e-s1s2+2s+e-4s4s3+1s L-1{H(s)}=L-11s2-e-s1s2+2s+e-4s4s3+1s…

Q: Find y': y = arc sec(x²) y = xVx - 1 2 y : xVI -x 2 y = xVx -1 x Vx - 1

A: Given: y=arcsec(x2)y'=dydx=ddx(arcsec(x2))We know that ddx(arcsec(u(x)))=11-1(u(x))2…

Q: A farmer can buy two types of plant food, mix A and mix B. Each cubic yard of mix A contains 20…

A: This question can be solved using the concept of linear programming.

Q: 1+tan-1x D. y = + sec-1xcsc¯1x + xsin-1x +V1 - x2 2-3tan-1x

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Q: Given: y = arctan sinh find y' at x 2 cosh 1 3(1+sinh 1) cosh 1 Oy = 1+sinh 1 cosh 1 1+sinh 1 %3D…

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